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MECHANISM 


OSSICLES   OF   THE    EAR 


MEMBRANA   TYMPANI. 


H.  HELMHOLTZ, 

PROFESSOR  OF  PHTSIOLOGY  IN  THE    rKIVEKSITY  OP  BERLTN,  PRrSSIA. 

TRANSLATED  FROM  THE  GERMAN,  WITH  THE  AUTHOR'S  PERMISSION, 

BY 

ALBERT  H.  BUCK  AiND  NORMAXD  SMITH, 

OF  NEW-YORK. 


AVITH    T-WELVE    ILLUSTRATIONS. 


NEW-YORK : 
WILLIAM     WOOD    &    CO.,    27    GREAT    JONES    STREET. 

1873. 


3 


NOTICE 


Prof.  Helmholtz's  essay  on  The  Mechanism  of  the  Ossicles  of 
THE  Ear  and  Membrana  Tympani,  originally  published  in  the  1st 
volume  of  PJluger''s  Archiv  fiXr  Fhysiologie,  Bonn,  1809,  is  the  only 
treatise  in  any  language  which  enters  fully  into  the  anatomical,  physio- 
logical, and  mathematical  aspects  of  the  question,  and  will  undoubtedly 
remain  for  many  years  to  come  the  authoritative  treatise  on  this 
subject. 

In  view  of  the  great  importance  of  this  essay  to  those  interested 
in  the  department  of  otology,  the  undersigned  have  attempted  to 
translate  it  into  English.  The  style  of  writing  of  the  distinguished 
physiologist  is  so  exceedingly  condensed  that  some  allowance  will  be 
made,  we  trust,  for  the  evident  lack  of  smoothness  in  the  English 
version. 

A.  IT.   P..  and  N.  S. 


•^06816 


CONTENTS. 


PAOB 

§  1.    Results  due  to  the  small  Dimensions  of  the  Audiioiy  Apparatus 9 

^  2.    Anatomy  of  the  Membrana  Tympani 16 

^  3.    Attachments  of  the  Hammer 23 

§  4.    Attachments  of  the  Anvil 32 

(Translated  by  Albert  H.  Buck.) 

§  5.    The  Movements  of  the  Stirrup 41 

§  6.    The  Concerted  Action  of  the  Bones  of  the  Ear 45 

§  7.    Mechanism  of  the  Membrana  Tympani 53 

§  8.    Mathematical  Appendix,  having  particular  Reference  to  the  Mechanism 

of  Curved  Membranes 03 

(Translated  by  Normand  Smith.) 


MECHANISM 


OSSICLES   OF  THE   EAR. 


Fkom  a  notice  found  among  the  papers  of  the  late  B.  Rie- 
mann,  and  recently  pnl)lis]ied  in  tlie  Zeitung  fur  rationelle 
Medhin^  we  learn  what  views  this  man  of  unusual  penetra- 
tion— alas !  too  soon  lost  to  science — took,  during  the  last 
months  of  his  life,  regarding  the  problems  of  physiological 
acoustics,  and  why  so  few  of  them  had  thus  far  met  with  a  solu- 
tion. And  here,  too,  we  find  that  he  had  discovered  the  true 
source  of  all  difficnlty,  and  the  one  toward  which  all  scientific 
efforts  must  henceforth  be  directed.  lie  proposes,  as  the  chief 
task  of  aural  mechanics,  to  explain  how  the  apparatus  of  the 
middle  ear  can  transmit  from  the  air  to  the  fluid  of  the  laby- 
rinth sucli  extraordinarily  fine  shades  of  vibration — as  we  know 
it  actually  does.  He  proves,  by  calculatioii,  that  the  excursions 
of  the  stirrup,  in  the  fainter  (though  yet  clearly  to  be  distin- 
guished) tones,  must  be  so  small  as  to  escape  detection,  even  witli 
the  highest  powers  of  our  modern  microscopes.  To  transmit 
regularly  and  accurately  vibrations  of  such  delicacy,  he  holds 
that  there  must  be  a  corresponding  accuracy  and  precision  in 
the  vibrations  of  the  transmitting  a})paratus. 

At  the  same  time,  he  says  he  will  be  obliged  to  oppose  in 
many  particulars  the  theory  of  the  mechanism  of  hearing  as 
developed  by  me  in  the  Lehre  der  Tonempjindunyen.  In 
this  connection,  I  must  remark  that  I  myself  at  the  time  consid- 


8  MECHANISM   OF  THE   OSSICLES   OF   THE   EAR. 

ered  the  descrijHion  of  the  vibrations  of  the  apparatus  of  the 
middle  ear,  as  given  in  cliapter  1,  section  6,  of  the  work  in 
question,  to  be  simply  ])reliminary,  and  gathered  from  for- 
eign sources.  It  was  impossible  for  me  at  the  time  to  make 
aiiv  investigations  of  my  own  into  this  question,  although  I  fully 
recognized  the  necessity  for  new  investigations.  In  the 
description  which  I  gave  in  the  same  work  I  adopted,  in 
its  most  essential  features,  the  theory  of  Edward  "Weber,* 
which,  compared  with  former  theories,  is  a  decided  advance. 
It  is,  in  the  main,  correct,  although  wanting  in  certain  details 
which  are  indispensable  to  its  completeness.  It  struck  me 
that  the  chief  difiiculty  in  this  theory  lay  in  the  existence  of  a 
joint  between  the  hammer  and  anvil.  According  to  Weber's 
description,  the  hannner  and  anvil  constitute  an  innnovable 
angular  lever,  whose  axis  of  rotation  is  drawn  through  the  pro- 
cessus Folianus  of  the  hammer  and  the  end  of  the  processus 
brevis  of  the  anvil.  But  how  was  the  existence  of  a  joint, 
surrounded  by  a  weak  and  loose  capsular  membrane,  allowing 
motion  in  all  directions,  possible  in  the  midst  of  a  lever  whose 
vil)rationsmust  needs  be  of  the  greatest  fineness  and  accuracy? 
As  soon  as  the  completion  of  my  work  on  physiological  optics 
afforded  me  time  for  other  investigations,  I  took  the  above  ques- 
tion into  consideration  and  had  obtained  nearly  all  of  the  fol- 
lowing residts  before  seeing  Riemann's  Notizen.f  The  solution 
of  the  ditticulties  was  obtained  by  a  closer  investigation  into 
the  mechanics  of  the  joints  and  attachments  of  the  bones  of 
the  ear,  and  proved,  in  fact,  to  be  entirely  different  from  the 
one  proposed  by  the  celebrated  mathematician.  Besides,  I 
must  oppose  his  statement  "  that  it  is  the  task  of  the  ap- 
paratus of  the  middle  ear  to  transmit  to  the  fluid  of  the 
lal)yrinth  the  changes  in  atmospheric  pressure  at  every  moment 
of  tiTue,  with  perfect  accuracy  and  constant  relative  strength," 
because  I  consider  this  in  nowise  proven  by  the  facts  of  the  case. 
Accuracy  in  perception  requires  only  that  every   tone  of    a 

*  Bericlite  liber  die  Verhandluiifjen  der  Konigl.  Sachs.  Ges.  d.  Wi.sscni- 
scliaften  zu  Leipzig.      Math.  Phys.  Klasse.      1851,  Mai  18,  S.  29-31. 

f  Sliort  notice  of  them  iu  the  lleidelber^er  Jahrbiiclier.  Jul^-  ^Gth  and  Au- 
;fU8t  9tli,  1807. 


MECHANISM   OF  THE    OSSICLES   OF   THE    EAR,  9 

given  pitch  should  cause  the  same  sensation,  both  in  kind  and 
intensity,  every  time  tliat  it  is  reproduced.  It  is  a  well-known 
fact  that  tones  of  a  certain  pitch  produce  an  uncommonly 
strong  impression  upon  the  ear.  AYe  shall  mention  further  on 
other  new  examples  ofj  abnormities. 

§1. 

Results  due  to  the  small  Dimensions  of  the  Auditory  Apparatus. . 

The  most  important  step  in  advance  made  by  Edward  Weber 
in  the  theory  of  the  transmission  of  sound  in  the  ear — a  step 
which  has  recei\'ed  much  less  consideration  than  it  deserves — 
seems  to  me  to  be  the  view  that,  in  the  transmission  of  sound- 
vibrations,  the  bones  of  the  ear  and  the  petrous  portion  of  the 
temporal  bone  are  to  be  considered  as  solid,  incompressible 
bodies,  and  the  fluid  of  the  labyrinth  as  an  incompressible  fluid. 
He  rightly  declares  that  in  the  case  of  these  bodies  and  fluids 
there  can  be  no  question  as  to  the  transmission  of  waves  of 
condensation  and  rarefaction,  but  that  the  bones  of  the  ear 
must  be  considered  as  solid  levers,  and  the  fluid  of  the  laby- 
rinth as  a  mass  only  to  be  moved  as  a  whole. 

I  shall  take  the  liberty  of  going  more  minutely  into  this 
special  topic,  inasmuch  as  it  forms  the  basis  of  the  subsequent 
investigations. 

If  in  an  elastic  medium,  be  it  a  solid,  fluid,  or  gas,  whose  three 
dimensions  are  inflnitely  extended,  there  be  produced  plane 
waves  answering  to  a  simple  tone,  these  will  })ass  througli  tlie 
elastic  mass  with  the  rajiidity  which  belongs  to  that  giveii  tone, 
and  produce  at  different  points  of  the  mass  either  displacement 
of  the  ultimate  ])articles,  or  even  condensation,  Avhere  it  is 
caused  by  longitudinal  vibrations.  If  at  a  given  point  of  the 
mass  tliere  are  particles  in  a  state  of  extreme  displacement  up- 
ward, at  the  same  moment  of  time,  there  will  be,  at  a  distance 
of  half  a  wave's  length,  particles  in  a  state  of  extreme  displace- 
ment downward ;  and  the  same  is  true  of  all  other  directions 
of  displacement.  Between  these  upper  and  lower  limits  of 
extreme  displacement — which  must  be  at  least  half  a  wave's 
length  apart,  as  we  have  seen — we  shall  find  in  a  continuous- 


10  MECHANISM   OF   THE   OSSICLES   OF  THE   EAR. 

line  of  transition  tlie  lesser  degrees  of  displacement  upward, 
the  zero  point  of  this  displacement,  and  the  lesser  degrees  of 
displacement  downward,  so  that  the  difference  in  displacement 
of  two  oscillating  jparticlcs^  whose  distance  from,  one  another 
is  infinitely  small  compared  with  the  wave-length,  is  itself 
infinitely  small  compared  with  the  entire  amplitude  of  displace- 
ment. If  we  limit  ourselves  in  such  a  case  to  the  consideration 
of  a  small  portion  of  the  vibrating  mass,  all  of  whose  dimen- 
sions shall  be  infinitely  small  compared  with  tlie  wave-length, 
then  all  the  relative  displacements  of  the  individual  points  of 
this  mass,  among  themselves,  will  be  infinitely  small  compared 
with  the  amplitude  of  the  entire  vibrations,  Avhich  in  their  turn 
must  be  considered  as  infinitely  small  compared  with  the  wave- 
length, where  sound  vibrations  are  regularly  produced.  These 
relative  displacements  of  the  individual  particles  of  the  small 
mass  (which  we  imagine  to  be  taken  out  from  the  whole) 
among  themselves  are,  therefore,  infinitely  small  magnitudes  of 
second  order  compared  with  the  wave-length,  and  infinitely 
•Bmall  magnitudes  of  first  order  compared  with  the  amj^litudes 
of  vibration,  and  with  the  linear  dimensions  of  the  small  mass 
to  which  they  belong :  that  is  to  say,  the  small  mass  acts  in  the 
present  instance  just  as  an  absolutely  immovable  body  would. 

The  conditions  remain  the  same  when  a  large  number  of 
plane  waves,  belonging  to  the  same  simple  tone,  pass  tlirough 
the  elastic  mass ;  and  also  when  spherical  waves  spread  them- 
selves through  it,  taking  their  start  from  any  centre  whatsoever 
of  excitement  within  the  mass,  excepting,  however,  in  the  im- 
mediate neighborhood  of  punctiform  or  linear  centres  of  ex- 
•citement,  whose  appearance,  however,  is  more  a  mathematical 
fiction  than  a  practical  reality. 

The  same  law  applies  also  to  solid  elastic  bodies,  provided 
their  substance  is  not  infinitely  extended  in  all  directions,  but 
has  limits  against  which  the  Avaves  of  sound  may  strike  and  be 
thrown  back  toward  the  centre  of  the  mass.  It  is  here,  however, 
presupposed  that  either  no  linear  dimension  of  the  vibrating 
mass  shall  be  very  small,  compared  with  the  wave-length,  or  that 
this  should  be  the  case  with  all  the  dimensions  of  the  vibrating 
anass  at  the  same  time,  so  that  no  one  of  them  should  be  very 


MECHANISM   OF   THE   OSSICLES   OF   THE   EAR.  11 

small  compared  with  the  others,  as  is  the  case,  for  instance,  in 
disks,  membranes,  rods,  and  strings. 

The  proof  of  these  laws  is  easily  deduced  from  the  well-known 
laws  respecting  the  form  and  mode  of  vibration  of  plane  waves 
— so  long,  of  course,  as  there  is  only  question  of  plane  waves  of 
simple  tones  in  masses  of  infinite  extent.  On  the  other  hand, 
the  influence  of  boundary-planes  (Grenzfliichen)  and  of  the  last- 
named  conditions  has  been  elucidated  by  Kirclioff,  in  his  trea- 
tise on  the  equilibrium  and  vibration  of  an  infinitely  thin  elas- 
tic rod.*  In  this  treatise,  it  is  true,  only  the  equilibrium  of 
such  elastic  masses  is  taken  into  consideration,  and  it  is  there 
proven  that  forces,  wliich  are  infinitely  small  compared  with 
the  constant  of  elasticity  of  the  body,  and  which  are  brought 
to  bear  partly  on  the  central  and  partly  on  the  superficial  por- 
tion of  the  elastic  mass,  cause  only  infinitely  small  relative  dis- 
placements of  such  particles  as  lie  within  finite  distance  of  each 
other,  so  that  the  diflferential  quotients  of  the  displacements, 
as  taken  from  the  co  ordinates,  also  remain  finite.  On  this 
last  point  the  question  chiefly  hinges.  For,  if  these  differential 
quotients  are  finite  magnitudes,  then,  in  masses  of  infinitely 
small  linear  dimensions,  the  relative  displacements  of  the  indi- 
vidual particles  are  infinitely  small,  compared  with  the  total 
absolute  displacements  which  such  masses  experience. 

The  above-mentioned  law,  wliich  Kirehoft*  has  demonstrated 
for  the  condition  of  equilibrium,  the  forces  involved  being  infi- 
nitely small,  may  also,  by  means  of  d'Alembert's  rule,  be  ap- 
plied to  the  condition  of  motion,  provided  the  accelerations 
which  the  particles  of  the  mass  experience  during  motion  are 
considered  as  the  forces  which  disturb  the  elastic  body.  These 
now,  when  they  belong  to  vibrations  whose  amplitude,  com- 
pared with  the  length  of  tlie  wave,  is  infinitely  small,  are  them- 
selves infinitely  small,  and  answer,  therefore,  to  Kirchoff's  ac- 
ceptation of  infinitely  small  f  disturbing  forces. 

*  Borcliardt's  Journal  fiir  reine  und  angewandte  Matliematik  LVI.,  in  g  1  of 
tlie  treatise  in  question. 

f  If  A  be  the  amplitude  of  vibration,  n  the  number  of  vibrations  of  a  sim- 
ple tone,  t  the  time,  and  c  a  constant  determining  the  phasis,  then  has  s,  the 
variable  departure  from  the  position  of  equilibrium,  the  following  value  : 

S  =  A  sin  I  2  TTut  -t-  c  [ 


12  MECHANISM   OF   THE   OSSICLES  OF  THE   EAR. 

The  law  demonstrated  by  Kjrcliofi',  and  applied  to  the  pres- 
ent case,  might  be  thus  expressed  : 

In  immovahU  elastic  bodies,  all  of  whose  linear  dimensions 
are  not  infinitely  small  compared  with  the  wave-length,  or  at 
least  none  of  which  are  infinitely  small  compared  with  the 
res,t,  vibrations  of  a  simple  ^o;ie,  whose  amplitude  is  infinitely 
small  compared  with  the  wave-length  of  the  same  kind  of  vibra- 
tions in  masses  of  infinite  \\\a\X.%, -produce  upon  two  poi7its  of  the 
elastic  body,  whose  distance  from  one  another  is  infinitely  small 
compared  with  the  same  wave-length,  relative  displacements, 
which  are  themselves  infinitely  small  compared  with  the  entire 
amplitude  of  the  vibrations. 

Tiiat  is  to  say,  then,  that,  under  the  restrictions  mentioned, 
masses  whose  linear  dimensions  are  all  small  compared  with  the 
wave-length  act  exactly  like  absolutely  solid  bodies  ;  or,  that 
the  changes  in  form  which  they  undergo  can  be  disregarded  when 
compared  with  the  entire  amplitude  of  their  vibrations. 

If  we  now  take  into  account  that  in  air  the  wave-lengths  of 
the  tones  constituting  our  musical  scale — that  is,  from  C,  witli 
33  vibrations  to  c  ^  with  4224  vibrations — vary  from  8  to  1000 
cm. ;  that  in  water  the  same  waves  are  more  than  4  times,  in 
brass  about  11  times,  in  copper  12  times,  in  steel  and  glass 
more  than  15  times  greater  than  in  air;  that,  on  the  other 
hand,  tbe  dimensions  of  the  bones  of  the  ear  and  of  the  laby- 
rinth  are  only  small  fractions  of  a  centimetre,  the  important 

If  //  re])resent  tlu;  volunu'  (if  the  small  part,  tlien  k,  the  power  used  to  ac- 
celerate the  same,  is  equal  to 

k  =  li  I'i  =  —  4  tt'  n*  A  sin  \  2  -nt  +  c  \ 

If  now  A  be  the  wave-lenjrth,  and  a  the  rate  of  progress  for  this  kind  of  vibra 
tioos  in  masses  of  unlimited  extent,  then 

__« 

and  for  the  maximum  of  k,  which  appears  as  often  as  the  sinus  of  the  for- 
mula given  for  it  equals  ±  1  : 

k  ,    ,     ,  A 

a  // 

k  is  therefore  infinitely  small  compared  with  a',  provided  A  is  infinitely  small 
compared  with  X;  and  «'  multiplied  by  the  density  is  equal  to  the  constant  of 
the  elastic  resistance,  which  in  this  kind  of  comparison  assumes  a  value. 


MECHANISM    OF   THE   OSSICLES   OF   THE    EAR.  13 

conclusion  follows' that  the  dimensions  of  the  elastic  solid  and  flnid 
masses,  constituting  the  organ  of  hearing  are  all  at  best  only 
very  small  fractions  of  the  wave-lengths  of  those  tones  which 
we  commonly  hear,  and  which  our  ear  can  readily  appreciate. 

We  are,  moreover,  to  conclude  from  what  has  already  been  said 
that,  in  the  vibrations  of  the  auditory  apparatus,  of  the  bones 
of  the  ear  and  of  the  petrous  bone,  caused  by  the  tones  ordi- 
narily appreciable  by  the  ear,  the  particles  of  each  of  these 
small  masses  undergo  displacements  among  one  another,  which 
are  infinitely  small  compared  with  the  amplitude  of  the  sound- 
vibrations  producing  tliem ;  that  is  to  say,  that  they  act  very 
nearly  like  absolutely  solid  bodies. 

The  final  reason  for  this  peculiarity  of  motion  is  to  be  found 
in  the  very  great  rapidity  with  which  the  influence  of  every 
shock,  communicated  to  one  of  these  small  solid  masses,  is  trans- 
mitted through  it.  This  rapidity  is  so  great  that  the  time 
required  for  transn)ission  of  the  shock  may,  as  a  rule,  be  con- 
sidered as  infinitely  small  wlien  compared  with  the  duration  of 
the  individual  sound-vibrations,  and  its  action  as  instantane- 
ously conveyed  throughout  the  entire  mass. 

An  incomj)ressib]e  fluid,  inclosed  within  solid  w^alls,  differs 
from  one  that  is  compressible  in  the  fact  that  here,  too,  every 
shock  communicated  to  one  part  of  its  superficies  is  instantlj'' 
transmitted  through  the  entire  fluid,  and  sets  every  portion  of  it 
instantaneously  in  motion ;  while  in  a  compressible  fluid  one 
wave  starts  from  its  point  of  origin,  runs  its  course  with  a  cer- 
tain speed,  and  sets  alternately  the  different  portions  of  the  fluid 
in  motion.  If,  therefore,  in  the  case  of  the  fluid  of  the  labyrinth, 
the  dimensions  of  the  whole  mass  are  infinitely  small  compared 
with  the  wave-length,  and  the  walls  of  the  petrous  bone  inclos- 
ing the  fluid  are  strong  enough  to  be  considered  as  absolutely 
immovable  beneath  the  small  pressure  exerted  in  this  instance 
against  tlieni,  then  the  transmission  of  tlie  shock  throughout 
the  entire  mass  is  practically  instantaneous,  and  the  fluid  of 
the  labyrinth  may  be  said  to  act  under  the  influence  of  vibra- 
tions of  sound  precisely  as  a  fluid  absolutely  incompressible, 
and  therefore  incapable  of  transmitting  the  vibrations  of  sound, 
would  do  under  the  same  circumstances. 


14  MECHANISM   OF  THE   OSSICLES  OF  THE   EAE. 

Finally,  it  is  necessary,  at  least  for  the  deeper  and  middle 
tones  of  tlie  scale,  that  there  shonld  be  an  equality  of  pressure 
between  the  air  contained  in  the  middle  ear  and  that  of  the  ex- 
ternal auditory  canal.  In  tlie  case  of  very  high  tones,  those 
corresponding  to  the  highest  octave  of  the  piano,  the  length  of 
the  auditory  canal  is  very  nearly  equal  to  a  quarter  of  a  wave's 
length,  to  which  circumstance  is  due  the  occurrence  of  those 
phenomena  of  resonance  described  by  me  in  the  Lelire  von  den 
To7iemj[>Jiiulunyen.^  At  all  events,  the  diameter  of  the  exter- 
nal auditory  canal  is  too  small  to  permit  of  difterent  phases  of 
pressure  or  of  speed  at  difterent  points  of  the  membrana  tym- 
pani  at  the  same  moment,  and  we  can,  therefore,  without  liesita- 
tion  consider  the  pressure  as  equal  at  all  times  over  all  parts  of 
the  membrane.  This  circumstance  is  likewise  of  great  impor- 
tance in  the  mechanism  of  the  ear,  for  it  excludes  all  possibility 
of  one  part  of  the  membrana  tympani  being  excited,  while 
the  rest  is  not ;  the  part  excited  being  dependent  on  the 
locality  of  the  sound-giving  body.  Hence  we  have  no  otlier 
means  of  localizing  sound  except  by  noting  the  diflierent  degrees 
of  intensity  obtained  by  changing  the  position  of  the  head  and 
comparing  the  impressions  made  upon  both  eai^s. 

The  above-mentioned  rule  applies,  as  already  stated,  to  bodies 
none  of  whose  linear  dimensions  are  infinitely  small  compared 
■viath  the  rest,  consequently  not  to  strings,  membranes,  rods,  and 
disks.  It  is  also  liable  to  exceptions,  as  where  the  middle  por- 
tion of  the  body  in  question  is  contracted  and  very  narrow. 
Among  the  component  parts  of  the  auditory  apparatus,  the  mem- 
brana tympani  is  the  only  one  which  falls  under  the  head  of 
exceptions.  In  point  of  fact,  those  bodies  which  are  very  thin 
at  one  spot,  or  in  one  direction,  are  capable  of  performing  com- 
paratively slow  vibrations ;  for,  owing  to  their  slight  tliickness, 
they  ofter  but  a  feeble  elastic  resistance,  return  slowly  to  a  state 
of  equilibrium,  and  vibrate  at  a  much  slower  rate  than  is  the 
case  with  oscillations  in  thick  masses  of  the  same  nature. 

That  the  bones  of  the  ear  do  not  come  under  the  head  of  ex- 
ceptions, is  easily  shown  by  comparing  them  with  the  metallic 
rods  or  tongues  which  are  used  in  the  i)rodu(;tion  of  high  tones. 
*  Pages  175, 176. 


MECHANISM    OF   THE   OSSICLES   OF   THE    EAR.  15 

The  tongues  eni ployed  to  produce  the  highest  tones  of  the  musi- 
cal scale  in  a  harmonium  are  relatively  very  long  and  thin  when 
compared  with  the  dimensions  of  the  hones  of  the  ear,  and  no 
one,  who  has  any  experience  in  the  tones  which  belong  to,  or 
can  be  produced  by  such  solid  bodies,  could  for  a  moment  doubt 
that,  were  it  possible  to  put  into  regular  vibration  such  small 
masses  as  the  bones  of  the  ear,  including  the  relatively  slender 
stirrup,  these  would  give  forth  tones  of  such  enormous  height 
that  to  our  ear  they  would  probably  no  longer  be  perceptible — 
tones  lying  far  beyond  the  limits  of  our  musical  scale. 

The  relation  sustained  by  the  bones  of  the  ear  to  the  vibra- 
tions of  sound  is  practically  the  same  as  in  an  iron  rod,  when 
hung  up  and  caused  to  vibrate  as  a  pendulum.  Such  a 
rod  is  elastic  and  yielding,  and  is  capable  of  several  kinds  of 
vibration  ;  but  these  vibrations  take  place  at  tlie  rate  of  several 
hundred  per  second,  while  as  a  pendulum  it  swings  perhaps 
only  once  in  a  second.  If  sueli  a  pendulum  is  caused  to  vibrate 
by  a  force  exercised  periodically,  the  periods  amounting  to  one 
or  more  seconds,  or  to  larger  fractions  of  a  second,  each  blow 
communicated  by  this  power  to  one  point  of  the  rod  can  traverse 
the  same  hither  and  thither  several  hundred  times  before  the 
blow  belonging  to  the  next  period  is  given,  and  thus  the  effect 
of  the  blow  can  be  transmitted  tlioroughly  to  every  part  of  the 
mass  before  even  a  small  fraction  of  the  period  of  a  vibration 
has  passed.  Under  these  circumstances  the  pendulum  vibrates 
practically  as  an  absolutely  solid  body,  that  is,  its  real  motion 
is  not  to  be  distinguished  from  the  motion  of  such  a  body, 
not  even  by  means  of  the  most  delicate  methods  of  observation. 
Entirely  different  is  the  action  of  the  pendulum  when  we  cause 
it  to  vibrate  by  means  of  a  tone  whose  pitch  approximates  that 
of  the  rod.  Then  it  vibrates,  no  longer  according  to  the  laws  of 
a  pendulum,  but  as  a  vibrating  elastic  rod. 

The  same  is  true  of  the  bones  of  the  ear.  As  long  as  the 
periods  of  vibration  of  the  tones  Avhich  these  must  transmit 
are  very  great  compared  with  those  of  the  bones  themselves, 
60  long  will  the  latter  act,  practically,  as  absolutely  solid 
bodies. 


16 


MECHANISM   OF  THE   OSSICLES   OF  THE   EAR. 


§2. 

Anatomy  of  the  Membrana  Tympani. 

Before  passinj^  on  to  the  discussion  of  the  mechanism  of  the 
apparatus  of  the  middle  ear.  I  must  make  one  or  two  anatomi- 
cal remarks,  not  with  tlie  view  of  bringing  forward  any  thing 
materially  new,  but  simply  to  give  prominence  to  a  number  of 
small  points,  which  as  a  rule  are  merely  noticed  and  then  pass- 
ed over  by  the  anatomist,  but  which  gain  importance  in  a  more 
thorough  investigation  of  their  physiological  bearings. 

The  opening  in  which  the  membrana  tympani  is  set  is  formed 
from  the  squamous  portion  of  tlie  temporal  bone  and  from  what 
was  once  the  annulus  tympanicus,  both  of  which  in  adults  are 
firmly  connected  by  a  bony  union  ;  not  so  firmly,  however,  but 
that  in  chiseling  out  a  preparation  of  the  ear,  a  l^reak  is  likely 
to  occur  at  this  very  spot  of  union — a  circumstance  which  I 
found  very  annoying  in  exposing  to  view  the  connections  of  the 
upper  part  ot  the  membrana  tympani.  Even  on  the  dried  adult 
bone  this  line  of  separation  is  still  pretty  clearly  marked  by  two 
prominent  bony  spurs,  which  rise  up,  before  and  behind,  on  the 
boundary  between  both  parts  ;    these  separate  a  lower   part, 

which  is  nearly  oval  in  form  and 
contains  a  rim  for  the  attachment 
of  the  membrana  tympani,  from 
an  upper  part,  whicli  is  irregular 
in  outline  and  more  strongly  con- 
cave. The  former  belongs  to  the 
OS  tympanicum,  the  latter  to 
the  OS  squamosum.  Fig.  1  re- 
presents the  upper  and  anterior 
wall  of  the  bony  portion  of  the 
external  auditory  canal.  The 
line  of  section  was  drawn  parallel 
to  this  wall,  ah  \'S,  the  surface  of 
section  of  the  anterior  wall,  which 
separates  the  auditory  canal  from  the  joint  of  the  jaw;  C6?is 
the  line  of  section  through  the  posterior  wall ;  h  d  is  the  outer 
opening  of  the  auditory  canal ;  a  slight  furrow  li  /,  which  in  the 


Fig.  1. 


MECHANISM   OF  THE   OSSICLES   OF  THE   EAE.  17 

engraving  is  more  strongly  marked  than  is  actually  the  case  in 
nature,  represents   the   line  of  attachment  of  the  membrana 
tympani.      Traces  of  the  fissure,  which  in  the  foetus  divides 
the  anterior  upper  border  of  the  annulus  tympanicus  from  the 
squamous  portion,  may  still  be  seen  running  from  the  point/' 
in  the  direction  of  g.     Between  a  and  h  the  same  fissure  (fissura 
Glaseri)   is  recognizable.    The  projecting  point   at  /",   which, 
plays  an  important  part  in  the  attachment  of  the  hammer,  is 
called  by  Henle  the  spina  tympanica  posterior,  in  contradistinc- 
tion to  another  more  distinctly  marked  point  in  the  foetus,  on 
the  anterior  end  of   the  annulus,  at  its  outer  anterior  angle,, 
which  he  calls  the  spina  tympanica  anterior,  and  which,  on  the 
much  broader  os  tympanicum    of  the   adult,  answers  to  the 
point  g.     The  latter,  however,  lies  flat  upon  the  corresponding 
surface  of  the  squamous  bone  and  no  longer  stands  out  as  a  spur. 
On  the  posterior  end  of  the  above-mentioned  recess,  and  corre- 
sponding to  a  point  in  Fig.  1  between  c  and  ^,  there  can  be  seen 
a  blunt  and  less  prominent  projection  of  the  rim,  in  wliicli  the. 
membrana  tympani  is  inserted,  which  we  shall  frequently  have 
occasion  to  speak  of  in  describing  its  attachments.     In  order  to- 
avoid  errors  which  might  arise  through  my  giving  Ilenle's  name 
of  spina  tympanica  posterior  to  the  anterior  point/",  I  shall  take 
the  liberty  of  applying  to  it  the  name  of  spina  tympanica  major, 
and  to  the  posterior  point  at  i  that  of  spina  tympanica  minor .. 
The  neck  of  the  hammer  fits  into  the  recess  lying  between/" 
and  c  in  such  a  manner  that  the  point  at  /  almost  touches  it.. 
The  line  of  attachment  of  the  membrana  tympani  also  shows  a 
slight  and  ill-defined  depression  where  it  passes  near  the  j)oints 
/and  i.    And  just  here,  moreover,  the  line  is  less  sharply  defined 
than  lower  down  on  tlie  part  formed  from  the  os  tynq)anicum  ; 
and  here,  too,  slight  pressure  with  a  blunt  instrument  will  loosen 
the  membrana  tympani  from  its  attachments.    In  fact,  it  is  more  • 
truly  attached  to  the  cutis  than  to  the  bone. 

This  recess  in  the  upper  border  we  shall  call  the  Rivinian  re- 
cess, as  it  includes  the  opening  described  by  Rivini,  an  opening 
which  represents  the  last  trace  of  the  original  visceral  cleft,  but 
which  in  the  majority  of  normal  adults  does  not  exist. 

Although  normally  no  opening  exists  there,  still  the  Rivinian. 
2 


18  MECHANISM   OF  THE   OSSICLES  OF  THE   EAR. 

I'ecess  is  filled  with  a  loose  part  of  tlie  drum-head,  which,  as  it 
iippears  beneath  the  thin  cutis,  is  seen  to  consist  of  bundles  of 
loosely  interwoven  connective  tissue,  which  give  passage  to  ves- 
sels and  nerves  and  are  easily  separated.  (Membrana  flaccida 
^hrapnell.)  For  this  reason,  abscesses  are  wont  to  perforate  at 
this  point,  and  here  too,  in  making  preparations  of  the  cutis 
layer,  artificial  openings  are  readily  made.  The  diiference  in 
tension  and  consistency  between  this  upper  part  of  the  drum- 
head and  the  rest  of  the  membrane  can  easily  be  felt  by  pass- 
ing the  blunt  end  of  a  sewing-needle  over  the  surface  of  the 
membrane,  in  a  preparation  where  the  attachments  of  the  bones 
and  of  the  membrana  tympani  are  still  undisturbed.  It  is  then 
readily  perceived  that  between  the  spina  tympanica  major 
and  minor  there  is  a  pretty  tense  cord  of  fibres,  into  which  the 
processus  brevis  of  the  hammer  is  inserted  in  a  direction  toward 
the  anterior  border.  This  cord  forms  the  upper  border  of  the 
lower  and  firmer  part  of  the  membrane.  As  soon  as  the  explor- 
ing needle  passes  beyond  it,  it  sinks  suddenly  into  the  Rivinian 
recess,  while  pressing  before  it  the  loose  cutis  and  mass  of  con- 
nective tissue.  And  if,  moreover,  we  examine  carefully  the 
vaulting  of  the  outer  side  of  the  membrana  tympani,  in  a  suit- 
able preparation  and  with  oblique  light,  we  can  generally  make 
out  this  cord  running  from  the  processus  brevis  mallei  toward 
the  spina  tympanica  minor.  As  far  as  I  could  ascertain,  this 
cord  is  formed  from  the  peculiar  tendinous  fibres  of  the  mem- 
brana tympani.  "We  shall  call  it  the  upper  cord  of  attachment 
of  the  membrana  tympani.  It  forms  the  boundary  for  that  part 
of  the  membrane  which  has  to  be  taken  into  consideration  in 
vibrations  of  sound. 

On  the  inner  side,  the  membrana  flaccida  is  continued  on  from 
its  line  of  insertion  into  the  tissue  of  the  fold  of  mucous  mem- 
brane which  forms  what  has  been  described  by  Troltsch  as  the 
posterior  pocket  of  the  membrana  tympani,  and  in  whose  lower 
free  border  lies  the  chorda  tympani.  The  line  of  insertion  of 
the  membrana  tympani  unites  with  that  of  the  above-mentioned 
fold  at  the  bottom  of  the  Itivinian  recess  ;  here  their  attachment 
to  one  another  is  stronger  than  to  the  bone ;  posteriorly,  how- 
t€ver,  the  line  of  insertion  of  the  fold  of  mucous  membrane  does 


MECHANISM   OF   THE   OSSICLES   OF   THE   EAR.  19 

not  run  parallel  with  that  of  the  merabrana  tympani,  but  pur- 
sues its  course  along  the  sharp  border  of  the  wedge-shaped  bony 
process  represented  by  c  in  Fig.  1.  The  outer  surface  of  this 
process  lies  parallel  with  the  membrana  tympani  and  a  sliort 
distance  to  the  inside  of  it,  and  can  even  be  seen  from  the  out- 
side as  a  whitish  object  shining  through  the  semi-transparent 
membrane.  Lower  down  on  tlie  border  of  this  process  is  the 
opening  wliich  gives  egress  to  the  chorda  tympani.  The  smaller 
recess,  which  can  be  seen  behind  the  sharp  border  near  c  in  Fig. 
1,  represents  a  section  of  the  funnel-shaped  projection  of  the  ca- 
nal of  the  chorda.  The  fold  of  mucous  membrane  forming  the 
posterior  pocket  of  the  membrana  tympani  reaches  down  as  far 
as  the  exit  of  the  nerve,  which  itself  fnrms  the  border  of  the 
pocket. 

The  line  where  the  fold  of  mucous  membrane  comes  in  con- 
tact with  the  membrana  tympani  runs  from  the  highest  point  of 
the  Rivinian  recess  forward  toward  the  processus  brevis  of  the 
hammer.  This  portion  of  the  fold  separates  the  smaller  anterior 
from  the  larger  posterior  pocket.  Its  line  of  attachment  on  the 
hammer  we  shall  describe  hereafter. 

Tlie  Rivinian  recess  lies  above  and  a  little  in  front  of  the 
membrana  tympani.  Its  greatest  diameter  extends  in  a  nearly 
perpendicular  line  downward  from  the  posterior  end  of  the  re- 
cess, above  the  spina  tympanica  minor.  I  have  measured  its 
length  in  a  number  of  specimens,  and  find  it  agrees  with  that 
given  by  Troltsch — 9  to  10  mm.  The  smallest  diameter  is  in  a 
nearly  horizontal  direction,  and  begins  somewhat  under  the  spina 
tympanica  major.  Its  length  I  found  to  be  from  7^  to  9  mm. 
These  measurements  are,  as  a  general  thing,  the  same  in  infan- 
tile skulls  as  in  those  of  adxilts. 

As  is  well  known,  the  inner  end  of  the  external  auditory  canal 
is  pointed  inward  and  a  little  downward ;  and,  besides,  the 
plane  that  passes  through  the  groove  in  which  the  membrana 
tympani  is  inserted  is  inclined  at  an  angle  of  55°  to  the  axis  of 
the  external  auditory  canal,  while  the  membranes  of  l)oth  sides 
form  with  each  other  an  obtuse  angle,  opened  upward,  of  130° 
to  135°. 

The  membrana  tympani  is  not  stretched  out  flat  in  the  ring 


20  MECHANISM   OF  THE   OSSICLES  OF  THE   EAR. 

to  whicli  it  is  attaclied,  but  its  centre  or  Jiavel  is  strongly  drawn 
inward  by  tlie  liandle  of  the  hammer,  with  -which  it  is  united; 
for  this  reason  the  membrane  has  the  shape  of  a  funnel  whose 
point  or  end  corresponds  to  the  tip  of  the  handle  of  the  hammer, 
and  whose  meridian  lines  are  convexed  toward  the  hollow  of 
the  funnel.  In  order  to  represent  this  form  of  the  membrana 
tympani,  a  point  of  great  importance  in  tlie  mechanics  of  the 
conduction  of  sound,  I  took  a  cast  with  stearin  of  the  upper  wall 
of  the  external  auditory  canal  and  of  the  outer  surface  of  the 
membrane,  after  having  first  removed  the  lower  wall  of  the 
canal,  without,  however,  disturbing  any  of  the  connections  of  the 

membrana  tympani.  Its  outlines  are 
represented  inFig.  2,  just  as  I  copied 
them  in  the  camera  clara ;  ab  is 
Fig.  2.  '^^''''^^^  the  upper  wall  of  the  external  au- 
ditory canal,  b  c  the  vertical  outline  of  the  membrana  tympani. 
From  the  figure  it  is  very  clear  that  the  radii  drawm  on  the 
surface  of  the  membrana  tympani  are  convexed  outward 
toward  the  external  auditory  canal.  At  the  same  time,  it  can 
be  seen  that,  as  a  result  of  this  drawing  in  of  the  navel,  the 
upper  half  of  the  membrane  is  made  to  lie  in  almost  the  same 
direction  as  the  upper  wall  of  the  canal,  while  the  lower  half 
stands  almost  at  a  right  angle  with  the  axis  of  this  canal.  This 
last  circumstance  is  of  importance  in  the  examination  of  the  ear 
with  the  reflector,  inasmuch  as  this  perpendicular  portion  of  the 
membrana  tympani,  which  is  situated,  as  a  rule,  just  below  the 
tip  of  the  manubrium,  reflects  back  through  the  external  audi- 
tory passage  the  light  that  is  thrown  in  upon  it,  and  thus  gives 
rise  to  the  triangular  "  bright  spot." 

The  outer  surface  of  tlie  membrana  tympani,  which  is  cov- 
ered with  an  epithelial  layer,  the  continuation  of  the  horny  epi- 
dermis of  the  skin  of  the  external  auditory  passage,  owes  its  pro- 
perty of  reflecting  light  to  the  fat  which  it  contains.  In  a  very 
fresh  specimen  of  the  ear,  drops  of  water  can  be  seen  running  off 
from  this  fatty  surface  as  from  oiled  paj^er. 

The  convexity  of  the  meridians  of  the  membrana  tympani  is 
least  at  that  meridian  in  which  the  handle  of  the  hammer  lies. 


MECHANISM   OF   THE   OSSICLES   OF  THE   EAR.  21 

The  outline  of  the  stearin  cast  answering  to  this  part  is  repre- 
sented in  Fig.  3,  the  position  of  the  hammer 
being  marked  by  dotted  Knes.     At  the  same 
time,  it  can  be  seen  in  this  drawing  that  the 
navel  lies  somewhat  nnderthe  true  centre  of  "^gTs. 

the  membrane. 

The  meridian  in  which  the  handle  of  the  hammer  lies  extends 
upward  and  forward  from  the  navel  toward  the  anterior  limit 
of  the  Rivinian  recess,  so  that  the  processus  brevis  of  the  ham- 
mer, which  forms  the  upper  limit  of  the  handle,  comes  to  lie 
nearly  back  of  the  &p\iv  which  is  situated  on  the  outer  side  of 
the  line  of  attachment  of  the  membrana  tympani,  and  Mdiich 
answers  to  the  inwardly  pointing  spina  tympanica  major.  To 
this  the  hammer  is  attached  partly  by  means  of  a  compact 
ligament  (ligamentum  mallei  anterius,)  and  partly  by  its  so- 
called  long  process,  (processus  Folianus.)  The  latter,  so  long  as 
it  exists,  lies  in  a  furrow  on  the  inner  border  of  the  process. 

While,  on  the  one  hand,  the  tip  of  the  manubrium  draws  the 
navel  of  the  membrana  tympani  inward,  on  the  other,  the  pro- 
cessus brevis  at  the  base  of  the  manubrium  tends  somewhat  to 
press  it  outward. 

The  membrana  tympani  consists  essentially  of  a  peculiar 
tendinous  membrane,  which,  although  only  one-twentieth  of  a 
millimetre  thick,  is  yet  comparatively  very  strong.  Externally 
it  is  clothed  with  a  thin  continuation  of  the  skin  of  the  external 
auditory  canal,  internally  by  a  thin  continuation  of  the  mucous 
membrane  of  the  middle  ear.  Taken  together,  these  layers  have 
a  thickness  of  0.1  mm.  The  outer  skin  layer  consists  principally 
of  a  continuation  of  the  epidermis,  supported  by  a  thin  layer  of 
loosely-woven  bundles  of  connective  tissue.  It  can  be  removed 
entire  from  the  greater  portion  of  the  surface  of  the  membrane, 
excepting  at  the  Rivinian  recess  and  along  the  handle  of  the 
hammer,*  where  it  is  more  closely  united  with  the  thickened  and 
cartilage-like  tissue  of  the  membrane.  From  the  lii  vinian  recess 
along  the  upper  wall  of  the  external  auditory  canal  there  runs 

*  Gruber's  obliquely  descending  fibres  of  the  membrana  tympani  unite  at  tluB 
point  with  the  fibres  of  the  cutis,  forming  in  a  mechanical  sense — although 
perhaps  they  must  be  separated  histologically — the  deepest  layer  of  the  same. 


22  MECHANISM   OF  THE  OSSICLES  OF  THE  EAR. 

a  line,  along  wliicli  the  skin  is  more  strongly  attached  to  the 
bone.  The  fibres  of  the  cutis  dip  down  here  into  the  fissura 
Glaseri,  Avhich  at  an  earlier  period  was  a  cleft  dividing  the 
squamous  portion  from  the  os  tympanicum,  (Fig.  1,  fg^ 

The  middle  and  stronger  layer  of  the  membrana  tympani  is 
fibrous,  and  consists  ])artly  of  radiating,  partly  of  circular  fibres. 
The  radiating  fibres  lie  on  the  outer  side,  the  circular  on  the 
inner  side  of  the  layer.  In  the  anterior  half  of  the  membrane 
the  radiating  fibres  proceed  from  the  tip  of  the  manubrium 
mallei  as  a  centre.  On  the  posterior  half,  however,  they  run 
nearly  parallel  to  each  other  from  the  entire  length  of  the 
manubrium.  Their  thickness  is  least  along  the  border  of  the 
membrane  and  grows  gradually  thicker  on  approaching  the 
end  of  the  manubrium,  where  they  are  packed  more  closely 
together. 

In  the  centre  of  the  membrane  the  circular  fibres  form  a  very 
thin  layer  which  gradually  increases  in  thickness  toward  the  peri- 
phery ;  at  the  extreme  periphery,  however,  they  disappear  alto- 
gether (according  to  Gerlach),  or  at  least  (according  to  J.  Gruber) 
form  a  very  much  thinner  layer  than  in  the  centre.  In  tlieHivinian 
recess  the  circular  fibres  are  strongly  developed  and  of  a  satin- 
like appearance ;  they  form  here  a  cord-like  boundary  for  the 
upper  side  of  the  firmer  part  of  the  membrana  tympani  and 
i  ntersect  at  a  very  small  acute  angle  the  radiating  fibres,  which 
at  this  point  radiate,  not  from  the  navel,  but  from  the  processus 
brevis  of  the  hammer.  Here,  too,  they  are  intermingled  with 
straggling  fibres  of  the  cutis. 

Tlie  tendinous  fibres  of  these  layers  are  very  dense  and  un- 
yielding, they  lie  close  to  one  another,  and  offer  very  great 
resistance  to  any  distending  force.  Through  their  great  power 
of  elastic  resistance  they  differ  materially  from  the  very  much 
more  yielding  yellow  elastic  tissue.  The  substance  of  the 
membrana  tympani  swells  in  acetic  acid  and  solutions  of  potash, 
as  is  the  case  with  tendinous  tissue,  but  not  with  the  elastic 
tissue.  I  found  that,  like  tendinous  tissue,  it  would  soon  dis- 
solve completely  in  a  boiling  potash  solution,  leaving  behind 
mere  traces  of  elastic  tissue,  consisting  partly  of  vessels,  and 
partly  of  a  very  thin  continuous  membrane — probably  the  base- 


MECHANISM   OF   THE   OSSICLES   OF  THE   EAR.  23 

ment  membrane  of  tlie  mucous  layer  on  the  inner  side  of  tlie 
merabrana  tympani. 

This  peculiarity  of  construction  of  the  membrana  tympani 
is  a  very  important  element  in  the  mechanical  working  of  this 
membrane,  as  we  shall  see  further  on.  It  is  not  to  be  considered 
as  an  elastic,  yielding  membrane,  but  as  an  almost  inextensible 
one..  Its  want  of  capacity  for  yielding  can  be  appreciated  when 
one  tries  to  tear  it  with  needles,  either  after  it  has  been  removed 
and  spread  out  upon  a  glass  slide,  or  while  it  still  remains  attach- 
ed in  its  natural  position.  It  cannot  be  drawn  out  like  a  piece 
of  rubber,  or  a  softened  animal  bladder,  but  offers  very  power- 
ful resistance  to  tension,  and  forms  folds  about  the  spot  that  is 
being  stretched,  as  in  a  collodion  membrane. 

§3. 
Attachments  of  the  Hammer. 

The  manner  in  which  the  hammer  is  attached  to  the  mem- 
brana tympani  has  been  thoroughly  described  by  J.  Gruber  in 
a  monograph  published  recently  by  him.  The  part  of  the 
membrana  tympani  corresponding  to  the  attachment  of  the 
hammer  is  thickened,  partly  by  strong  fibres  of  the  cutis  layer 
extending  from  the  Rivinian  recess  along  the  manubrium,  partly 
by  an  accumulation  of  fibro-cartilaginous  tissue.  The  perios- 
teum of  the  hammer,  along  both  surfaces  of  the  manubrium, 
is  continuous  with  the  fibro-cartilaginous  layer,  whose  borders 
are  thus  closely  united  to  the  hammer.  Near  the  lower  end  of 
the  manubrium  the  union  between  the  bone  and  the  thickened 
tissue  of  the  membrana  tympani  is  very  close;  near  the  pro- 
cessus brevis,  however,  a  looser  layer  intervenes  between  the 
bone  and  the  membrane,  or  there  may  even  be  a  kind  of  incom- 
plete joint-space,  which  is  limited  on  both  sides  by  the  closer 
union  between  the  periosteum  of  the  hammer  and  the  borders 
of  the  cartilao-inous  laver,  tog-ether  with  the  fibrous  tissue  of  the 
membrana  tympani. 

Tlie  hammer  by  means  of  its  handle  draws  the  navel  of  the 
membrana  tympani  inward  ;  to  maintain  a  close  union  between 
these  two  parts  the  connection  between  them  should  be  strongest 
at  this  point.    At  the  processus  brevis  the  hanmier  simply  presses 


24 


MECHANISM   OF  THE   OSSICLES  OF  THE   EAR, 


against  tlie  membrana  tjmpani;  consequently  here  a  less 
intimate  union  suffices,  while  at  the  same  time  it  aiFords  a 
possibility  for  slight  motions  of  the  hammer  upon  the  mem- 
brane, a  necessity  whose  conditions  we  shall  investigate  more 
thoroughly  further  on. 

The  second  and  relatively  strongest  attachment  of  the  ham- 
mer is  to  the  spina  tympanica  major.  The  end  of  this  spur 
extends  close  up  to  the  neck  of  the  hammer,  into  the  hollow  at 
<?,  (Fig.  4,)  just  above  the  root  of  the  processus  Folianus.  The 
hammer,  in  this  sketch,  is  seen  from  the  outside ;  cjp  is  the 
head,  h  the  processus  brevis,  m  the  handle,  *  the  articular  sur- 
face for  the  reception  of  the  anvil.  The  processus  Folianus  lies 
along  tlie  inner  border — that  turned  toward  the  tympanum — of 
the  spina,  (the  marginya  of  Fig.  1,)  so  that  between  Z,  the  end 
of  the  processus  Folianus,  and  the  hollow  at  rZ,  the  border  of  the 
spina  and  the  corresponding  border  of  the  processus  Folianus  run 
almost  parallel  to  each  other,  with  a  space  intervening  between 
them  of  about  |-mm.  From  the  upper  sur- 
face of  tlies  pina  a  bony  margin  extends  uj)- 
ward  in  such  a  manner  as  to  fit  pretty 
closely  to  the  side  of  the  hammer  between 
d  andy,  the  intervening  space  between  the 
hammer  and  the  bony  margin  being  con- 
tinuous with  the  space  previously  mentioned 
and  of  the  same  width  with  it.  This  entire 
fissure  is  bridged  over  with  short  and  tense 
ligamentous  fibres  ;  longer  fibres  of  the  same 
kind  start  from  the  surface  of  the  spina  and 
from  its  downward  projecting  border,  and, 
converging  toward  the  point  d  of  the  ham- 
mer, envelop  both  the  lower  border  and  the  outer  surface  of  tlie 
processus  Folianus,  so  that  it  lies  completely  hidden  in  this  mass 
of  tendinous  fibres  which  forms  the  ligamentum  anterius  mal- 
lei and  is  covered  by  a  fold  of  mucous  membrane. 

As  for  the  processus  Folianus  of  the  hammer,  I  must  remark 
that  in  children  it  is  a  long  elastic  blade  of  bone  extending  as 
far  as  to  the  fissura  Glaseri.  As  regards,  however,  its  condition 
in  adults,  I  must  side  with  those  wlio  describe  it  as  having 


MECHANISM    OF   THE    OSSICLES    OF  THE    EAR.  25 

dwindled  down  to  a  short  stump.  I  would  state  that,  in  prepar- 
ing a  number  of  temporal  bones,  I  took  particular  care  to  no- 
tice whether  this  process  was  not  perhaps  broken  oif  in  the 
attempt  to  loosen  the  hammer.  To  ascertain  this,  before  the 
hammer  had  been  at  all  disturbed  in  its  natural  position,  I 
searched  for  the  processus  Folianus  with  the  point  of  a  fine 
needle,  inserting  it  as  a  probe  between  the  fibres  of  the  ligamen- 
tum  anterius  mallei.  In  this  way  I  could  follow  it  distinctly 
for  a  short  distance,  when  it  came  abruptly  to  an  end  in 
the  midst  of  the  anterior  ligament,  and  1  could  feel  nothing 
like  a  continuation  of  the  bony  blade,  which  would  have  been 
present  if  the  process  had  simply  been  broken. 

I  must  remark,  moreover,  that  this  remaining  stump  of  the 
processus  Folianus  does  not  lie  in  immediate  contact  with  the 
bony  mass  of  the  spina;  it  is  attached  to  it  throughout  by 
means  of  short  fibrous  bands.  Hence  in  a  specimen  where  the 
hammer  retains  its  natural  position,  and  all  of  its  attachments 
are  preserved  entire,  it  is  possible,  by  pressing  upon  the  base  of 
the  processus  Folianus  with  the  point  of  a  needle,  to  move  this 
part  of  the  hammer  not  only  upward  and  downward  but  also 
backward  and  forward,  as  far  as  the  short  fibrous  bands  of 
the  ligamentum  anterius  will  permit.  The  contact  of  bone  with 
bone,  if  it  existed  here,  would  ofier  an  obstacle  to  any  one  of 
these  motions. 

If  we,  therefore,  leave  out  of  the  account  the  longer  supei*fi- 
cial  fibres,  the  ligamentum  anterius  mallei  appears  in  the  main 
to  be  a  very  short  and  broad  band  whose  line  of  insertion  ex- 
tends from  I  tof  on  the  hammer  (Fig.  4) ;  from  Itod  it  lies 
opposite  the  inner  border  of  the  spina  tympanica  major,  but 
near  the  point  d  it  is  nearly  opposite  to  a  bony  ridge  which  ex- 
tends from  d  on  the  spina  upward  toward  f.  I  must  add, 
moreover,  that,  above  and  below,  this  band  becomes  lost  in 
a  fold  of  mucous  membrane.  Above,  tlie  fold  of  raucous 
membrane  follows  pretty  closely  the  contour  of  the  bone 
(see  Fig.  4) ;  it  is  here  sickle-shaped  and  quite  thin,  because 
here  the  outer  wall  of  the  tympanum  is  everywhere  in  close 
proximity  to  the  head  of  the  hammer.  This  fold  of  mucous 
membrane  finally  terminates  on  the  upper  surface  of  the  head 


26  MECHANISM    OF    THE   OSSICLES   OF  THE    EAR. 

of  tlie  liamnier,  and  in  its  border  lies  the  short,  round  ligamen- 
tum  mallei  superius,  which  descends  obliquely  downward  and 
outward  upon  the  head  of  the  hammer.  Its  office  is,  there- 
fore, to  restrain  all  motions  of  the  latter  outward. 

The  ligaraentum  anterius  is  prolonged  downward  from  I  into 
two  folds  of  mucous  membrane,  one  of  which  runs  from  the 
base  of  the  processus  Folianus  toward  tlie  point  h  of  the  process- 
us brevis.  Its  opposite  line  of  insertion  lies  on  the  membrana 
tympani.  This  is  the  fold  wliich  separates  the  anterior  from 
the  posterior  pocket  of  the  membrana  tympani,  dividing  them 
in  such  a  way  that  the  space  above  the  processus  brevis  belongs 
chiefly  to  the  posterior  pocket.*  The  second  prolongation  of 
the  liganientum  anterius  downward  is  a  thin  fold  with  a  free 
margin,  which  follows  the  lower  border  of  ?,  (after  having  en- 
veloped this  process,)  and  then  continues  down  along  the  con- 
tour of  the  bone  as  far  as  to  the  tendon  of  the  tensor  tympani 
muscle  (Fig.  4).  In  the  drawing  this  spot  corresponds  to  where 
the  curved  line  at  5  meets  the  contour  line  of  the  bone.  This 
last-named  fold  is  a  limit  between  the  anterior  pocket  and  the 
cavity  of  tlie  tympanum. 

From  the  present  group  of  ligaments  and  mucous  folds, 
which  in  Fig.  4  follows  always  the  contour  line  of  the  bone 
from  h  to  c^,  and  at  d  is  composed  of  the  shortest  and  strongest 
fibres,  a  second  group  branches  off  at  d,  to  which  I  shall  give 
the  name  of  liganientum  mallei  externum.  It  springs  from 
a  ratlier  prominent  bony  ridge  on  the  hammer,  which  may  be 
seen  extending  from  d  to  c  in  Fig.  4,  and  is  inserted  into  the 
sharp  border  of  the  Rivinian  recess  ;  at  the  same  time  it  follows 
posteriorly  the  line  of  attachment  of  the  posterior  pocket  of  the 
membrana  tympani  (hence  in  Fig.  1,  from/"  to  c  along  the  con- 
tour line  of  the  drawing).     This  ligament  consists  of  a  number 

*In  tlie  "Archiv  fiir  Olirenlieilkunde,"  vol.  iii.,  pages  255-266,  Dr.  Prussack 
has  given  a  description  of  the  pockets  of  the  membrana  tympani,  which  dif- 
fers from  this.  He  describes  the  space  above  the  processus  brevis  of  the  ham- 
mer as  a  special  upper  pocket,  separated  from  the  posterior  pocket  by  a  parti- 
tion wall ;  I  have  never  been  able  to  find  such  an  one.  The  supposed  entrance 
into  this  pocket,  above  and  in  front  of  the  top  of  the  head  of  the  hammer, 
leads  into  the  space  above  the  liganientum  mallei  externum,  and  therefore  not 
at  all  to  the  membrana  tympani. 


MECHANISM    OF    THE    OSSICLES   OF  THE   EAR. 


27 


of  distinct,  satin-like,  tendinous  fibres,  whicli  radiate  from  the 
short  crest  of  the  hammer  (lying  between  d  and  c)  toward 
the  much  broader  curved  line  of  attachment  on  the  temporal 
bone. 

In  Fig.  5,  this  ligament  is  represented  as  seen  from  above ; 
e  g  \s>  its  line  of  attachment  to  the  temporal  bone.  The  tympa- 
num in  this  preparation  was  opened  from  above,  and  its  upper 
and  outer  wall  suificiently  chiseled  away  to  permit  of  a  free 
view  between  this  wall  and  the  surface  of  the  bones  facing  it. 


m  is  the  head  of  the  hammer,  i  the  body  of  the  anvil,  hi  the 
end  of  its  short  process,  and  Tu  the  entrance  to  the  tube.  Deep 
down  a  jjart  of  the  stirrup  St  can  be  seen,  and  the  tendon  of  its 
muscle  M.st^  and  further  on  the  tendon  of  the  tensor  tympani 
with  the  funnel-shaped  osseous  canal  from  which  it  issues. 
Gh.Th  the  chorda  tympani,  whicli  marks  the  free  border  of  the 
folds  of  mucous  membrane  limiting  the  ])ockets  ;  at  /  are  the 
upper  fibres  of  the  ligamentum  mallei  anterius,  which  arise 
above  the  spina  tympanica  major  SjJ.t.  The  prominent  crest 
on  the  neck  of  the  hammer,  from  which  the  fibres  of  the  liga- 
mentum externum  radiate,  is  here  distinctly  visible. 

The  stronofest  and  most  tense  bundle  of  fibres  of  this  last- 
named  ligament  is  the  posterior  one,  which  is  inserted  at  g. 
The  line  of  the  direction  which  it  follows,  when  continued, 
passes  through  the  end  of  the  spina.  It  is  also  this  bundle 
which  represents  chiefiy  the  axis  of  rotation  of  the  hammer. 
I  prefer,  therefore,  to  call  this  posterior  group  of  fibres  of  the 


28  MKCHANISM    OF   THE    OSSICLES   OF  THE   EAR. 

ligamentum  exteniutn  by  the  special  name  of  ligamentum 
mallei  postieiim,  because  in  a  mechanical  sense  it  has  indeed  a 
special  importance.  In  a  specimen  where  all  the  attachments 
of  the  ossicles  remain  undisturbed,  the  great  tension  of  these 
posterior  fibres  can  be  distinctly  felt  by  pressing  upon  them  with 
the  point  of  a  needle  ;  at  the  same  time  the  border  of  the  fold 
of  mucous  membrane,  in  which  the  chorda  tympani  lies,  will 
always  be  found  in  a  relaxed  condition  ;  and  moreover  tlie  an- 
terior bundle  of  fibres  of  the  ligamentum  externum  (at  e  in 
Fig.  5)  is  never  very  tense  unless  the  tensor  tympani  is  in  a 
state  of  contraction,  or  the  membrana  tympani  is  being  forced 
outward.  By  pressing  harder  with  the  needle  upon  the  chord 
of  the  ligamentum  posticum,  the  hammer  can  be  made  to  in- 
cline appreciably.  In  forcing  the  membrana  tympani  inward 
or  outward,  it  is  this  very  group  of  fibres  of  the  ligamentum 
externum  which  moves  the  least  of  all  the  attachments  of  the 
hammer.  The  I'eason  for  this  slight  displacement  will  appear 
further  on. 

If  we  suppose  the  line  of  direction  of  the  ligamentum  posti- 
cum continued  on  through  tlie  liammer,  it  will  be  found  to  meet 
and  run  in  the  same  direction  with  the  middle  and  strongest  fibres 
of  the  ligamentum  anterius  which  take  tlieir  origin  from  the 
spina  tympanica  major.  These  two  sets  of  fibres,  which,  al- 
though separated  by  the  intervening  body  of  the  hammer,  are 
still  in  a  mechanical  sense  one  band,  we  may  call  the  axis-band 
of  the  hammer.  This  band  alone  is  sufficient  to  hold  the  ham- 
mer in  its  natural  position,  even  after  the  anvil  has  been  care- 
fully separated  from  it ;  but  if  the  tendon  of  the  tensor  tym- 
pani be  still  tense,  this  position  will  then  be  really  quite  firm. 
In  Fig.  4,  the  approximate  position  of  the  axis  of  the  hammer 
is  marked  by  a  dotted  line  a  a. 

The  cords  forming  the  anterior  portion  of  the  ligamentum 
externum  (Fig.  5,  e)  are  made  up  of  shorter  fibres  which  are  di- 
rected outward  toward  the  edge  of  tlie  membrana  tympani, 
where  it  is  attached  at  the  bottom  of  the  Ilivinian  recess.  As 
they  lie  above  the  axis  of  the  hammer,  they  oppose  any  move- 
ment of  the  manubrium  mallei  or  of  the  membrana  tympani 
outward  toward  the  external  auditory  canal.     Hence  their  es- 


I 


MECHANISM    OF    THE    OSSICLES   OF  THE   EAR.  29 

sential  office  is  to  restrain  the  rotation  of  the  manubrium  out- 
ward. In  a  suitable  preparation,  like  that  of  Fig.  5,  this  fact 
can  be  readily  verified.  When  the  membrana  tympani  is  press- 
ed inward,  or  the  head  of  the  hammer  outward,  these  fibres 
become  relaxed.  They  allow  only  a  slight  rotation  of  the  ma- 
nubrium outward,  even  after  the  tendon  of  the  tensor  tym- 
pani, the  stapedo-incudal  joint,  and  the  ligamentum  superius 
mallei  have  been  divided.  By  pressing  upon  these  same  fibres 
from  above  with  the  blunt  end  of  a  needle,  and  thereby  putting 
them  on  the  stretch,  the  inclination  of  the  membrana  tympani 
inward  will  be  increased.  Finally,  it  must  be  remarked  that, 
whenever  the  tensor  tympani  is  strongly  stretched,  the  manu- 
brium mallei  is  prevented  from  being  drawn  further  inward 
by  the  tense  condition  of  the  membrana  tympani,  while  the 
axis-band  of  the  hammer  is  prevented  from  being  pulled  inward 
beyond  a  certain  limit  by  the  above-mentioned  set  of  fibres  of 
the  ligamentum  externum  ;  when  these  become  tense  the  limit 
has  been  reached.  At  ,this  point,  the  traction  of  the  tensor 
tympani  will  be  transferred  to  these  fibres,  and  can  no  longer 
affect  the  axis-band. 

While  the  ligamentum  externum,  on  the  one  hand,  protects 
the  axis-band  of  the  hammer  from  being  pulled  too  strongly 
inward,  the  upper  and  lower  fibres  of  the  ligamentum  anterius, 
on  the  other  hand,  prevent  it  from  being  drawn  too  strongly  up- 
ward or  downward.  If  the  hammer  were  to  rotate  about  its 
attachment  to  the  spina  as  a  centre,  with  its  head  backward 
and  the  end  of  the  manubrium  forward,  the  upper  fibres  of  the 
ligamentum  anterius  would  be  put  upon  the  stretch ;  and  if  in 
the  opposite  direction,  the  lower  fibres.  Hence  it  happens 
that,  even  after  the  anvil  has  been  removed,  the  ligaments 
hitherto  described  remain  unaffected,  the  hammer  is  still  able  to 
resist  any  such  inclinations,  and  remains  jjretty  steady  in  its  natu- 
ral position.  The  uppermost  fibres  of  the  ligamentum  anterius 
usually  approach  the  head  of  the  hammer  in  an  inward  direc- 
tion, (as  can  be  seen  in  Fig.  5  at/",)  and  hence,  like  the  liga- 
menta  superius  and  externum,  they  become  tense  when  the 
membrana  tympani  is  pushed  outward. 

The  tension  of  these  ligaments,  in  the  natural  state  of  things, 


ki  i 


30  MECHANISM    OF   THE   OSSICIiES   OF    THE   EAR. 

is  increased  by  tlie  elastic  force  of  the  comparatively  strong 
miisculus  tensor  tympani,  whose  tendon  is  attached  to  the  ham- 
mer on  the  anterior  half  of  its  inner  side  facing  the  tube,  at  the 
commencement  of  the  manubrium,  and  a  little  lower  down  than 
where  the  processus  brevis  projects  from  the  side.  In  Fig.  9, 
the  line  of  insertion  of  this  tendon  is  shown  extending  from 
above  obliquely  downward  and  backward.  The  muscle,  as'is 
well  known,  lies  in  a  special  bony  canal  whose  course  runs  pa 
rallel  with  and  above  the  Eustachian  tube,  by  means  of  which 
the  cavity  of  the  tympanum  communicates  with  the  pharynx. 
The  further  end  of  the  muscle  arises  outside  of  this  canal,  from 
the  under  surface  of  the  pyramidal  portion  of  the  petrous  bone 
and  from  the  cartilaginous  portion  of  the  Eustachian  tube.  It 
then  proceeds  through  its  appropriate  canal,  whose  open  end, 
toward  the  cavity  of  the  tympanum,  terminates  in  a  spoon-like 
process ;  around  this  the  tendon  of  the  muscle  passes,  and  then 
finally  crosses  the  cavity  of  the  tympanum  obliquely  {Tt^  Fig.  5) 
toward  its  point  of  insertion  on  the  hammer.  The  direction 
followed  by  the  tendon  is  nearly  perpendicular  to  the  plane 
drawn  through  the  border  of  the  membrana  tympani,  so  that 
its  line  of  traction  varies  only  a  little  downward  and  forward 
from  such  a  perpendicular.  On  the  other  hand,  it  forms  a  mo- 
derately acute  angle  with  the  lower  portion  of  the  handle  of 
the  hammer  and  with  the  anterior  portion  of  its  axis  of  rotation. 
The  tensor  tympani  is  a  penniform  muscle;  it  originates 
from  the  periosteum  of  the  upper  wall  of  the  canal  in  which  it 
lies ;  its  tendon  lies  next  to  the  under  surface  of  the  canal,  and 
presents  a  free,  smooth  surface  to  tlie  smooth  periosteum.  The 
muscular  fibres  are  rather  short,  and  hence  the  tendon  extends 
back  to  the  very  end  of  the  canal.  The  periosteal  tube  which 
sheathes  the  muscle  is  continued  orer  the  tendon  in  its  course 
through  the  cavity  of  the  tympanum ;  its  outer  surface  is  there 
covered  with  the  mucous  membrane  of  that  cavity.  Toynbee 
calls  this  free  part  of  the  sheath  the  tensor  ligament  of  the 
membrana  tympani.  The  separation  of  the  tendon  from  its 
sheath — if  we  compare  the  descriptions  of  difterent  observers — 
seems  to  be  more  or  less  complete ;  in  an  anatomical  collection 
of  this  city  I  have  seen  a  specimen  where  the  perfectly  smooth 


MECHANISM    OF  THE    OSSICLES   OF   THE    EAR.  31 

tendon  was  surrounded  by  a  perfectly  free  sheatli,  just  as 
Toynbee  describes  it ;  in  microscopic  sections,  however,  Ilenle 
has  seen  the  two  united  by  pretty  strong  bands  of  connective 
tissue.  As  the  hammer,  however,  requires  exceedingly  little 
space  for  its  excursions,  there  is  no  need  whatever  that  the  ten- 
don should  have  much  room  for  motion. 

The  tensor  tympani  draws  the  handle  of  the  hammer,  and 
with  it  the  membrana  tympani,  inward,  thereby  putting  the 
latter  on  the  stretch.  This  action  can  be  readily  seen  on  a  spe- 
cimen where  the  canal  of  the  muscle  and  the  cavity  of  the  tym- 
panum have  been  opened  from  above.  By  pulling  upon  the 
tendinous  fibres  of  the  muscle  within  the  canal,  the  membrana 
tympani  becomes  tense.  As  the  point  of  insertion  of  the 
muscle  lies  but  a  trifle  lower  down  than  the  axis-band  of  the 
hammer,  the  band  itself  will  also  at  the  same  time  be  stretched 
inward,  and  especially  the  posterior  portion  of  it,  the  ligamen- 
tum  mallei  posticum,  which  lies  very  nearly  in  the  same  line 
with  the  line  of  traction  of  the  tensor  tympani.  The  position 
of  the  hammer  is  thus  made  quite  firm,  even  though  the  tendon 
be  but  moderately  tense.  We  must  remember  here  that  a 
slight  traction,  when  made  at  right  angles  to  the  length  upon 
an  inextensible  cord  which  is  already  tense,  can  very  materially 
increase  its  tension ;  and  also  that  during  life  a  muscle  in  a 
state  of  rest  must  be  considered  as  a  very  yielding,  though  al- 
ways slightly  tense  elastic  band,  whose  tension  can  be  very  con- 
siderably increased  by  active  contraction.  Aside  from  the  fact 
that  the  tensor  tympani,  on  account  of  its  penniform  construc- 
tion, is,  mechanically  speaking,  equivalent  to  a  muscle  of  much 
greater  diameter  and  shorter  length  of  fibre,  we  can  consider 
its  simple  elastic  traction,  without  the  occurrence  of  any  ac- 
tive contraction  whatever,  as  a  pretty  important  power. 

In  this  way  it  is  clear  that  the  hammer,  so  long  as  it  retains 
its  natural  attachments — although  these  be  but  yielding  bands 
— and  even  after  the  division  of  the  stapedo-incudal  joint,  is 
capable  of  only  a  limited  motion  in  the  direction  of  rotation 
about  the  above-mentioned  axis;  and  that  any  attempts  to 
move  it  in  a  different  direction  meet  with  very  strong  resis- 
tance.    Anteriorly  its  axis  is  held  securely  by  the  ligamentum 


32  MECHA^■ISM   OF  THE   OSSICLES  OF  THE   EAR. 

antcrius,  and  the  processus  Foliaiius,  which  is  embedded  in  its 
meshes  ;  posteriorly  by  the  posterior  fibres  of  the  ligamentum 
externum :  the  two  togetlier  we  liave  called  the  axis-band  of 
the  hammer.  Tliis  is  always  pretty  tense,  even  after  the  tendon 
of  the  tensor  tympani  has  been  divided ;  but  if  the  latter 
draws  upon  the  axis-band  at  a  right  angle,  its  tension  then  be- 
comes very  great. 

The  hammer  thus  fastened,  possesses,  besides  the  tendon  of 
the  tensor  tympani,  the  following  bands,  capable  of  restraining 
any  rotation  of  the  handle  outward  :  1.  the  middle  and  ante- 
rior fibres  of  the  ligamentum  externum,  2.  the  ligamentum 
superius,  3.  the  upper  fibres  of  the  ligamentum  anterius.  The 
inembrana  tympani  itself  acts  as  a  band  of  restraint  against 
too  strong  rotation  of  the  handle  of  the  hammer  inward. 

As  far  as  the  slight  yielding  capacity  of  the  axis-band 
and  of  the  upper  (relatively  lower)  fibres  of  the  ligamentum 
anterius  will  allow,  the  head  of  the  liammer  can  incline 
forward  and  backward,  or  rotate  about  a  vertical  axis. 
Nevertheless,  when  the  hammer  is  connected  with  the  anvil 
these  motions  are  thereby  still  further  limited.  Still,  we  shall 
see  that  the  motion  of  the  hammer  and  anvil  together  requires 
a  certain  amount  of  yielding  capacity  on  the  part  of  the  axis- 
band. 

Attachments  of  the  Anvil. 
The  body  of  the  anvil  is  united  to  the  hammer  through  the 
medium  of  a  joint.  Its  long  process  extends  downward,  and 
has  at  the  end  (which  is  bent  somewhat  inward)  a  small  articu- 
lar surface  for  the  stirrup.  The  short  process  extends  back- 
ward, and  its  extremity,  on  whose  lower  aspect  there  is  a  small 
incomplete  articular  surface,  lies  in  an  appropriate  hollow  cut 
out  of  the  bony  wall  of  the  tympanum,  at  a  point  where  the 
cavity  of  the  latter  merges  into  that  of  the  cells  of  the  mastoid 
process.  The  capsule  of  this  joint,  on  it  supper  surface  at 
least,  is  composed  of  strong  tendinous  fibres  which  extend  in- 
ward, backward,  and  outward  from  the  short  process  (see  Fig, 
5,  hi).  In  the  same  figure,  i  represents  the  body  of  the  anvil, 
and  *  the  capsular  ligament  of  the  malleo-incudal  joint. 


MECHANISM    OF   THE    OSSICLES   OF   THE    EAR. 


83 


The  shape  of  the  hist-nanied  articiihar  surface  is  usually  de- 
scribed as  resembling  a  saddle ;  it  must  be  remarked,  however, 
that,  unlike  the  saddle,  not  only  the  convex  sides  come  together 
to  form  a  ridge  that  is  almost  sharp,  but  also  the  concave ;  and 
the  union  of  the  two  forms  a  continuous  and  almost  flat  surface 
on  either  side  of  the  ridge.  In  order  to  gain  a  clear  idea  of 
the  mechanism  of  this  joint,  it  is  better,  I  believe,  to  make  use 
of  a  different  comparison  than  that  of  the  surface  of  a  saddle. 
It  is,  in  fact,  like  the  joint  used  in  certain  watch-keys,  where  the 
handle  cannot  be  turned  in  one  direction  without  carrying  the 
steel  shell  with  it,  while  in  the  opposite  direction  it  meets  with 
only  slight  resistance.  As  in  the  watch-key,  so  here  the  joint 
between  hammer  and  anvil  admits  of  a  slight  rotation  about 
an  axis  drawn  transversely  through  the  head  of  the  hammer 
toward  the  end  of  the  short  process  of  the  anvil ;  a  pair  of  co^s 
oppose  the  rotation  of  the  manubrium  inward,  but  it  can  be 
driven  outward  without  carrying  the  anvil  with  it. 

If  such  a  joint  had  to  be  constructed  of  metal,  we  should 
make  use  of  screw-surfaces.  A  hollow  cylinder,  cut  as  A  is 
represented  in  Fig.  0,  and  upon  which  the  y-;!.-^-^'""'^--''::;-^.. 

piece  B  (marked  in  dotted  lines)  fits,  would  (  \.  B  )  ] 
represent  the  normal  shape  of  such  a  joint.  |  f  ""-■■^-■■""^"- "f  I 
It  is  clear  that  A  and  B,  revolving  in  the        \"\  I  \ 

direction    of  tlieir  res})ective    arrows,    must        I  i  \  \ 

necessarily  strike  against  each  other  with 
their  cogs  a  and  h ,'  hence,  in  this  direction 
tlieir  rotation  is  limited.  In  the  opposite 
direction,  however,  their  rotation  is  free,  and 
is  accompanied  by  a  slowly  increasing  sepa- 
ration of  the  two  cylinders.  The  mechanic, 
in  making  such  a  joint,  usually  employs  a 
hollow  cylinder,  because  in  the  neighbor- 
hood of  the  axis,  were  the  cylinder  solid, 
the  screw  surface  would  incline  uj)ward  at  a 
pretty  steep  angle,  like  the  inner  border  of  a 
winding  staircase,  and  hence  would  be  difficult  to  execute. 
The  articular  ends  of  the  bones,  which  are  covered  with  a  layer 
of  elastic  yielding  cartilage,  filling  out  all  the  irregularities  of 
3 


FJK  0. 


34 


MECHANISM   OF  THE   OSSICLES   OF  THE   EAR. 


surface,  show,  as  a  (general  rule,  only  a  modified  form  of  the  above 
geometrical  outlines," one  where  the  margins  are  rounded  oif,  etc. 
The  periphery  of  the  m all eo-in cud al  joint  is  not  a  regularly  form- 
ed screw  outline.  If  we  imagine  it  rolled  out  upon  a  plane  from 
the  cylindrical  circumference  of  the  joint,  it  would  have  more 
or  less  the  form  represented  in  Fig.  7,  where  the  ends  «„  «,  are 
naturally  continuous.  Near  the  axis  of  the  joint  the  surface 
assumes,  not  exactly  the  shape  of  a  screw  as  in  a  winding  stair- 
case, but  rather  more  that  of  a  cone.  If  we  suppose  straight 
lines  to  be  drawn  from  a  point  in  the  axis  of  the  cylinder  to  all 
points  of  the  line  of  circumference  «„  «,,  we  shall  obtain  an  ap- 
proximate idea  of 
the  shape  of  the 
joint  in  question. 
In  the  case  of  the 
hammer,  we  would 
have  to  place  the 
apex  of  the  cone 
thus  formed  somewhat  lower  down  than  the  straight  part  of  the 
line  J„  «„  a^  &„  so  that  this  portion  of  the  surface  of  the  cone 
would  be  concave  on  the  hammer,  while  on  the  anvil  the  cor- 
responding part  is  convex.  Such  a  joint  may  therefore  be  said 
to  consist  of  four  nearly  plane  surfaces,  which  come  together 

at  its  centre,  and  along  its  l^order 
show  the  following  margins :  1. 
^0  c„  2.  c„  J„,  3.  c.  h„  4.  \  a,  a,  i„ 
while  the  upward-turned  surface 
of  the  joint,  like  a  saddle,  shows 
two  salient  borders  c„  and  J„  and 
two  reentering  Z»„  and  c,. 

In  Fig.  8,  the  hammer  is  rep- 
resented as  it  appears  from  above 
and  inside.  The  letters  aJ„  c„  J,  c, 
have  the  same  meaning  as  in  Flo;. 
7.  The  fiat  portion  of  the  arti- 
cular surface  is  seen  foreshortened.  P.F.  is  the  stump  of  the 
processus  Folianus  ;  Cr.,  the  commencement  of  tlie  bony  crest 
from  which  the  ligamentum  mallei  posticum  arises  ;  T.t.h  the 


I 


Fiff.  8. 


MECHANISM    OF   THE   OSSICLES   OF   THE    EAR.  35 

tendon  of  the  tensor  tympani.  As  can  be  seen,  the  part  a 
«,  lies  on  the  upper  side  of  the  malleo-inciidal  joint,  while  the 
line  of  junction  of  the  two  cogs  c„c,  lies  lower  down  between 
the  handle  of  the  hammer  and  the  .long  process  of  the  anvil ; 
the  cog  <?„  of  the  hammer  lies  on  that  side  of  the  joint  wliicli 
is  turned  toward  the  membrana  tympani ;  the  cog  of  the 
anvil,  on  tlie  median  side.  The  handle  of  the  hammer  cannot 
therefore  rotate  inward  without  carrying  the  anvil  with  it ;  the 
limit  of  rotation  outward  is  governed  by  the  flexibility  of  the 
ligaments  and  cartilaginous  covering  of  the  articular  surfaces. 

In  the  articular  surfaces  of  both  ossicles  the  point  a^  «,  lies 
at  a  greater  distance  from  the  axis  than  the  border  of  the  cog 
c„  (?, ;  ill  other  words,  that  portion  of  the  surfaces  which  is  nearly 
plane  is  greater  than  the  surfaces  of  the  cogs,  and  consequently 
the  entire  surface  of  the  joint  is  elliptical  in  shape,  with  the 
longer  axis  running  vertically.  It  should  be  stated,  furthermore, 
that  the  apex  of  the  cone-shaped  articular  surface  (we  have 
assumed  the  cone  to  be  the  type  of  this  joint  surface)  does  not 
come  to  a  point,  but  is  rounded  off,  as  in  a  saddle. 

A  conical  surface,  such  as  may  be  made  by  aid  of  Fig.  7, 
cannot  be  made  to  revolve  upon  its  exact  counterpart  without 
loss  of  contact  at  some  point ;  for  when  the  two  screw 
lines  h^  c„  and  5,  c,  glide  upon  each  other  at  the  periphery  of  the 
joint,  the  central  portion  of  the  joint  and  the  more  level  portion 
will  separate  each  from  the  corresponding  portion,  leaving  the 
two  bones  in  contact  only  at  the  above-mentioned  screw  lines. 
Since  the  working  space  in  such  a  motion  is  very  small,  there- 
fore we  may  readily  perceive  that  in  a  fresh  specimen  a  com- 
pressible cartilage  may  quite  fill  it. 

This  peculiar  mechanism  of  the  joint  can  be  readily  seen 
in  dry  specimens  of  the  ossicles;  one  match  may  be  fastened 
with  sealing-wax  to  the  head  of  the  hammer,  just  above  and  ini 
the  same  direction  with  the  processus  Folianiis,  and  another 
to  the  anvil,  at  the  end  of  its  processus  brevis,  and  in  the  same 
direction  with  it;  by  using  these  matches  as  handles,  and 
bringing  the  two  articular  surfaces  together,  the  hammer  may 
be  rotated  about  its  match  as  an  axis,  while  the  anvil  is  simply 
pressed  lightly  against  it.     If  the  hammer  is  rotated  in  the 


36  MECHANISM   OF   THE    OSSICLES   OF   THE    EAR, 

direction  from  the  liead  toward  the  short  process  and  liandle,  it 
will  grasp  the  anvil  very  tinnly,  and  compel  it  to  follow.  When 
the  hammer  is  rotated  in  the  opposite  direction,  the  two  articular 
sm'faces  at  once  separate  from  each  other  and  the  anvil  remains 
stationary. 

The  two  articular  surfaces  are  kept  in  contact  at  their  peri- 
pheries by  a  capsular  band  which  is  inserted  into  grooves  in  the 
bone  at  various  points  surrounding  the  joint.  This  capsular 
•band  is  not  very  strong  ;  it  tears  when  the  ossicles  are  exposed 
to  comparatively  slight  strains.  Of  this  band  the  strongest 
iibres  are  those  which  proceed  from  the  cog  of  the  hammer ; 
-at  this  point,  too,  a  few  fibres  of  the  ligamentum  externum  of  the 
hammer  pass  over  to  the  anvil.  The  length  of  an  excursion  of 
the  malleo-incudal  joint,  measured  at  the  lower  end  of  the  long 
process  of  the  anvil,  amounts  to  about  half  a  millimetre;  and 
this  point  being  nearly  6  millimetres  distant  from  the  axis  of 
the  joint,  the  rotation  of  the  two  ossicles  upon  each  other  will 
hardly  reach  5'^. 

So  long  as  the  hammer  and  anvil  retain  their  natural  con- 
nections with  each  other,  and  with  the  petrous  bone,  (the  anvil, 
however,  being  separated  fi'oin  the  stirru}),)  they  may  rotate 
•conjointly  in  such  a  manner  that  the  handle  of  the  hammer,  the 
long  process  of  the  anvil,  and  the  membrana  tympani  will  all  at 
the  same  time  move  either  inward  or  outward.  The  hammer 
by  itself  would  rotate  about  its  axis-band  as  axis,  but  owing  to 
its  connection  with  the  anvil,  this  mode  of  rotation  is  somewhat 
modified.  It  will  be  noticed,  in  the  first  place,  that  the  short  pro- 
cess of  the  anvil  (Fig.  5,  hi)  is  attached  to  the  petrous  bone  at  a 
point  considerably  to  the  inside  of  the  prolonged  axis  band  of 
the  hammer.  In  a  simple  rotation  about  a  fixed  axis,  only  those 
ipoints  are  at  rest  which  are  in  the  very  axis  of  rotation.  The 
distance,  furthermore,  of  any  individual  points  in  the  rotating 
body,  that  are  situated  outside  of  the  axis  of  rotation,  from  an 
external  fixed  point,  cannot  remain  unchanged  during  rotation; 
in  the  present  case  the  fixed  point  is  where  the  short  process  of 
the  anvil  is  attached  to  the  petrous  bone.  The  only  exception 
io  this,  however,  is  in  the  case  of  infinitely  small  rotations,  where 
ihose  points  of  the  rotating  body,  that  lie  in  a  plane  carried 


MECHANISM   OF   THE   OSSICLES   OF   THE   EAR.  37 

through  the  axis  of  rotation  and  the  external  fixed  point,  remain 
at  the  same  distance  from  that  lixed  point.  This  is  not  the 
case  with  the  head  of  the  hammer,  Avhich  is  situated  above  the 
axis  of  rotation  ;  hence, when  the  handle  of  the  hammer  is  rotated 
inward,  the  head  will  be  lifted  away  from  the  point  where  the 
short  process  of  the  anvil  is  bound  down.  Now,  inasmuch  as 
the  anvil  is,  so  to  speak,  suspended  by  pretty  short  and  rather 
unyielding  bands  between  the  head  of  the  hammer  and  the 
above-mentioned  point  of  attachment,  and  inasmuch  as  it 
maintains  an  immovable  position,  the  rotation  of  the  handle  of 
the  hammer  inward  must  be  accompanied  by  a  slight  inclina- 
tion of  the  head  backward  toward  the  anvil,  simultaneously 
with  a  motion  of  the  handle  forward.  That  such  an  inclina- 
tion of  the  head  backward  actually  does  take  place,  may  be  in- 
ferred from  the  tension  that  is  visible  during  rotation  in  the 
capsular  ligament  at  the  upper  side  of  the  malleo-incudal  joint, 
in  the  uppermost  libres  of  the  ligamentum  mallei  anterius,  and 
in  the  bands  which  give  firmness  to  the  tympano-ineudal  joint. 
By  pressing  the  membrana  tympani  inward  with  the  head  of  a 
pin,  we  can  see,  with  an  ordinary  magnifying-glass,  that  these 
two  capsular  ligaments  become  tense  the  moment  the  pressure 
is  exerted.  Furthermore,  if  we  press  Avith  a  needle  upon  the 
.short  process  of  the  anvil,  while  the  membrana  tympani  is  thus 
being  pushed  inward,  we  shall  feel  and  see  that  this  process 
does  not  lie  in  contact  with  the  bottom  of  tlie  shallow  groove  in 
which  it  fits,  but  is  lifted  slightly  above  it,  and  that,  when  we 
bring  this  process  into  contact  with  the  groove  by  pressure  from 
above,  the  upper,  satin-like  accessory  ligaments  of  .the  joint 
become  relaxed,  and  are  thrown  into  folds.  On  the  other  hand, 
the  tip  of  this  short  process  lies  in  contact  witli  the  wall  of  the 
tympanum,  which  rises  up  on  its  outer  side ;  its  connections, 
moreover,  with  this  outer  wall  are  such  that  it  can  glide  a  little 
upon  the  latter  in  a  vertical  direction.  At  the  same  time,  the 
anvil  is  held  suspended  free  in  the  air  by  the  hammer,  so  that 
in  its  normal  position  it  comes  in  contact  with  bone  only  at  the 
outer  side  of  the  end  of  the  short  process.  If,  however,  the 
handle  of  the  hammer  and  the  membrana  tympani  are  forced 
outward,  the  tip   of  the  sliort  process  of  the  anvil  will  glide 


38  MECHANISM   OF  THE   OSSICLES   OF   THE   EAR. 

down  into  its  appropriate  groove  in  the  bone  and  will  press  upon 
it  with  its  under  surface. 

With  a  joint  of  this  nature,  a  slii^-lit  displacement  must  neces- 
sarily take  ])lace  between  the  hannner  and  anvil  whenever  the  end 
of  the  handle  of  the  hammer  is  driven  inward.  If  we  imagine 
for  a  moment  the  anvil  and  hammer  immovably  joined  together, 
and  the  latter  made  to  revolve  about  its  axis-band,  the  end 
of  the  short  process  of  the  anvil,  lying  out  of  the  line  of  this 
axis,  will  necessarily  be  lifted  from  its  bed  wdienever  the  mem- 
brane of  the  drum  is  driven  inward.  To  lower  the  end  of  the 
short  process  again  and  bring  it  back  to  its  place,  the  anvil 
must  rotate  slightly  on  the  hammer.  A  limited  degree  of  such 
motion  is  possible  from  the  saddle-shape  of  the  malleo-incu- 
dal  joint.  At  the  same  time  the  long  process  of  the  anvil 
approaches  slightly  the  handle  of  the  hammer.  This  latter 
motion  can  be  observed  on  specimens  where  the  stapedo-incudal 
joint  has  been  severed,  while  all  the  other  connections  remain 
undisturbed.  It  is  just  in  this  position  of  the  two  ossicles,  more- 
over, that  the  lower  parts  of  the  joint  surfaces,  which  are  here 
armed  witli  teeth,  press  most  upon  one  another  (see  Fig.  8). 
This  can  be  ascertained  to  be  a  fact  by  placing  the  two  dry  os- 
sicles together  in  the  manner  described  above  and  noticing 
in  which  position  they  lit  the  closest. 

The  nature  of  this  joint  further  requires  a  slight  displacement 
on  the  part  of  the  hammer.  If  its  head  must  incline  toward 
the  anvil,  it  cannot  do  so  without  drawing  the  axis-band 
away  from  a  straight  line.  The  anterior  side  of  the  neck  with 
the  ])rocessus  Folianus  and  ligamentum  anterius  would  have  to 
be  lifted  up,  while  the  posterior  side  of  the  neck  Avith  the  pos- 
terior fibres  of  the  ligamentum  externum  were  being  drawn 
down.  The  first  of  those  motions,  however,  could  hardly  take 
place  on  account  of  the  spina  tympanica  posterior,  which  lies 
immediately  above  the  processus  Folianus,  and  against  which  the 
latter  would  at  once  strike.  All  the  more  marked,  then,  would 
have  to  be  the  sinking  of  the  posterior  side  of  the  neck,  and,  with 
it,  of  the  entire  hammer,  thus  causing  a  greater  tension  of  the 
fibres  of  the  lig.  mallei  post,  which  run  from  the  hammer  in  a 
backward  and  somewhat  upward  direction. 


MECHANISM    OF   THE    OSSICLES   OF   THE    EAR.  39 

These  views  are  in  harmony  with  a  short  notice  recently  pub- 
lished by  Politzer.*  He  attached  line  glass  rods  as  levers  to  the 
ossicles  in  order  that  he  might  determine  more  accurately  their 
individual  axes  of  rotation.  He  put  the  ineml)rana  tympani  in 
motion  hy  compressing  the  air  in  the  external  auditory  canal. 
In  this  way  he  ascertained  that  the  axis  of  rotation  of  the  ham- 
mer runs  through  the  end  of  the  processus  Folianus,  and  that  of 
the  anvil  through  the  extremity  of  its  short  process,  but  that 
both  of  these  axes  are  movable. 

It  appears  to  me  that  it  is  in  a  great  measure  owing  to  the 
slight  changes  in  the  axis  of  the  hammer,  caused  by  the  pecu- 
liar nature  of  the  anvil's  attachments,  that  the  navel  of  the  mem- 
brana  tympani  always  moves  in  a  normal  direction  relatively  to 
the  plane  of  insertion  of  this  membrane.  For  inasmuch  as  the 
axis  band  of  the  hammer  is  situated  obliquely  to  the])lane  of  in- 
sertion of  the  membrana  tympani,  every  motion  of  the  manu- 
brium mallei  inward  would  also  at  the  same  time  produce  a 
slight  displacement  of  the  navel  of  the  membrane  backward. 
But,  through  the  medium  of  the  anvil,  the  head  of  the  hammer 
is  at  the  same  time  drawn  backward,  thereby  causing  a  motion 
of  the  handle  forward  in  the  opposite  direction. 

Again,  the  navel  of  the  membrana  tympani  lies  at  a  greater 
distance  from  the  plane  of  insertion  of  this  membrane  than  tlie 
axis  of  rotation  of  the  hammer,  (excepting,  possibly,  its  extreme 
anterior  end  at  the  spina  tympanica,)  so  that  every  motion  in- 
ward of  the  manubrium  would  also  carry  the  navel  of  the  mem- 
brana tympani  a  little  upward  (that  is,  in  the  direction  of  the 
head  of  the  hammer).  This  upward  motion  is  counteracted,  as  we 
have  just  described  above,  by  the  circumstance  that  the  hammer 
as  a  whole  is  drawn  somewhat  downward  by  the  anvil  (in  a  rota- 
tion inward  of  the  manubrium). 

In  this  manner,  therefore,  both  these  deviations  are  corrected 
in  the  motion  of  the  navel  of  the  membrana  tympani ;  the  oidy 
kind  of  motion  that  remains  to  it,  then,  is  that  which  takes  place 
in  a  direction  at  right  angles  to  the  plane  of  insertion  of  the 
membrana  tympani. 

At  the  same  time  it  will  be  apparent  that  in  these  displace- 

*  Wochenblatt  der  K.  K.  Gesellscliaft  der  Aerzte.     Wien,  18G8,  Januar  8. 


40  MECHANISM    OF   THE   OSSICLES   OF   THE    EAR. 

ments  of  tlie  liainmer  its  short  process  nnist  glide  a  little  upon 
the  inembrana  tyinpani.  Such  a  gliding  motion  is  rendered 
possible  by  the  peculiar  manner  (described  by  J.  Gruber)  in 
which  these  two  parts  are  attached  the  one  to  the  other. 

I  would  like,  furthermore,  to  call  attention  to  the  fact  that, 
by  the  contraction  of  the  tensor  tyrapani  muscle,  all  the  bands 
wliicli  give  firmness  to  the  position  of  the  ossicles  are  rendered 
tense.  This  muscle,  in  the  first  place,  draws  the  handle  of  the 
hammer  inward,  and  with  it  the  membrana  tympani.  At  the 
same  time  it  pulls  upon  the  axis-band  of  the  hammer,  drawing 
it  inward  and  putting  it  upon  the  stretch.  Another  effect,  as 
we  have  shown,  is  to  draw  the  head  of  the  hammer  away  from 
the  tympano-incudal  joint,  to  tighten  all  the  ligaments  of  the 
anvil,  those  toward  the  hammer  as  well  as  those  at  the  end  of 
its  short  process,  and  to  lift  the  latter  up  from  its  bony  bed.  In 
this  way  the  anvil  is  brought  into  the  position  where  the  cogs  of 
the  malleo-incudal  joint  fit  into  one  another  the  tightest.  Fi- 
nally, the  long  process  of  the  anvil  is  compelled  to  perform  a  ro- 
tation inward  in  company  with  the  handle  of  the  hammer  ; 
in  so  doing,  as  we  shall  see  further  on,  it  presses  upon  the  stir- 
rup and  drives  it  into  the  oval  window  against  the  fluid  of  the 
labyrinth. 

In  this  respect  the  construction  of  the  ear  is  very  remarkable. 
By  the  contraction  of  the  single  mass  of  elastic  fibres  constitut- 
ing the  tensor  tympani  (whose  tension,  besides,  is  variable  and 
may  be  adapted  to  the  wants  of  the  ear)  all  the  inelastic  tendi- 
nous ligaments  of  the  ossicles  are  simultaneously  put  upon  the 
stretch. 

The  only  ligament  that  is  thereby  relaxed  is  the  ligamentum 
mallei  superins,  whose  influence  as  a  ligament  is  essentially  in 
the  same  direction  as  that  of  the  tendon  of  the  tensor  tympani. 

Hence,  if  we  examine  a  freshly  prepared  specimen  of  the  ear 
in  which  the  rigor  moi'tis  is  still  manifest  in  the  tensor  tympani 
muscle,  we  shall  find  every  thing  in  the  tympanum  stiff  and  un- 
yielding; whereas  later,  if  we  attempt  to  separate  the  different 
parts,  we  shall  find  that  almost  all  the  bands  and  ligaments  of 
the  ossicles  are  loose  and  relaxed;  in  fact,  without  a  careful  in- 


MECHANISM    OF   THE   OSSICLES   OF   THE    EAR.  41 

vestigation  of  the  relations  of  these  parts,  we  should  be  at  a  loss 
how  to  harmonize  the  two  conditions.* 


The  Movements  of  tJie  Stirrwp. 

The  joint  of  the  anvil  and  stirrup  resembles  the  fiat  segment 
of  a  sphere  which  is  convex  toward  the  stirrup.  The  capsule 
is  soft,  and  interwoven  more  with  elastic  fibres  than  the  two 
other  articulations ;  on- its  inferior  side  there  are  compact  fibres 
which,  when  the  anvil  is  drawn  upward,  are  put  on  the  stretch 
and  carry  the  anvil  with  them,  but  when  the  reverse  movement 
takes  place,  are  folded  together  so  tliat  the  anvil  does  not  follow 
so  closely  as  before. 

The  base  of  the  stirrup  is  surrounded  by  a  lip  of  elastic  fibro- 
cartilage  resemljling  the  li])s  of  cotyles  and  of  larger  articula- 
tions :  it  has  a  breadth  of  0.7  mm.  The  union  between  the 
base  of  the  stirrup  and  the  wall  of  the  labyrinth  appears  to  be 
formed  by  means  of  the  periosteum  of  the  vestibule,  which  perios- 
teum is  extended  over  the  base  of  the  stirrup.  The  fibrous  lip 
of  the  stirrup  is  not  attached  to  the  sides  of  the  fenestra 
ovalis. 

The  mucous  membrane  of  the  cavity  of  the  tympanum  ex- 
tends also  over  the  outer  side  of  the  joint.  The  attachments  of 
the  base  of  the  stirrup  along  its  straight  edge  are  more  tense  on 
the  inferior  than  on  the  superior  surface,  and  most  compact  at 
the  posterior  end.     Now,  if  you  apply  a  pin  to  that  side  of  the 

*  In  rejrard  to  the  question  wlien  the  tensor  tympani  contracts,  I  would  con- 
firm in  this  place  the  recently  published  observation  of  Politzer,  that  it  occurs 
durin<if  the  act  of  yawnint^f.  Before  hearing  of  his  experiments,  I  had  already 
noticed  that  whenever  I  attempted  to  restrain  the  motion  of  the  jaws 
during  the  act  of  yawning,  I  would  first  hear  the  well-known  hnapping  noise^ 
indicative  of  the  opening  of  the  tube  ;  then,  at  the  acme  of  the  yawn,  I  would 
notice,  in  addition  to  the  sense  of  tension  in  the  ear,  a  loud  muscular  noise, 
greater  even  in  intensity  than  that  produced  by  the  most  powerful  contractions 
of  the  masticator  muscles  during  closure  of  the  meati,  and  certainly  greater  tliau 
when  tlie  meati  are  open.  All  sounds  from  without  appeared  at  the  same  timo 
to  be  muffled.  From  these  observations  I  concluded  that  contraction  must  have 
been  excited  in  a  muscle  whose  oscillations  are  communicated  to  the  organ  of 
hearing  with  far  greater  distinctness  than  those  of  any  other  muscle  :  I  refer 
to  the  tensor  tympani. 


42  MECHANISM    OF   THE  OSSICLES  OF  THE  EAR. 

base  of  the  stirrup  wliicli  is  toward  the  vestibule  and  press  it 
outward,  it  will,  tliough  separated  from  the  anvil,  make  at  the 
same  time  a  lever-like  movement  by  which  its  head  is  pushed 
downM'ard  and  backward.  If  you  employ  a  fine  scAving-nee- 
dle  as  a  lever  of  sensation  and  press  it  into  the  base  of  the  stir- 
rup, the  lever-like  movement  can  be  still  better  observed.  In 
other  respects  the  mobility  of  the  base  of  the  stirrup  is  very 
slight.  I  have  calculated  it  partly  by  direct  observation  and 
partly  from  the  movement  of  the  water  of  the  labyrinth.  For 
the  purpose  of  direct  calculation  I  employed  a  preparation  in 
which  the  cavity  of  the  tymi)anuni  and  the  vestibule  had  been 
opened  from  above. 

The  })reparation  was  held  firmly  in  a  vice  in  such  a  position 
that  the  base  of  the  stirrup  looked  downward.  The  point  of 
a  fine  sewing-needle  was  then  inserted  into  the  membrana  ob- 
turatoria,  near  the  anterior  limb  of  the  stirrup  ;  the  needle  had 
for  its  second  fulcrum  the  sharply  cut  edge  of  \vhat  remained  of 
the  osseous  wall  between  the  cavity  of  the  tympanum  and  the 
labyrinth.  This  ]>oint,  3.8  mm.  removed  from  the  point  of  the 
needle  which  was  lixcd  in  the  ligainentum  obturatorium,  served 
as  the  centre  of  motion  for  the  lever-like  movements.  The  free 
portion  of  the  needle,  M'liich  was  horizontal,  formed  the  second 
longer  arm  of  the  lever,  (length,  23  mm.).  The  point  of  this 
longer  arm  moved  backward  and  forward  0.20  mm.,  when  the 
stirrup  was  pressed  inward  and  outward  by  means  of  a  needle 
applied  to  its  base  ;  and  .15  mm.,  when  the  pressure  was  made 
by  alternately  condensing  and  rarefying  the  air  in  th€  external 
meatus,  whereby  the  movement  of  the  membrana  tympani  was 
transmitted  through  the  other  bones  of  the  car  to  the  stir- 
rup. 

Now,  since  the  movements  of  the  stirrup  seemed  magnified, 
at  the  free  end  of  the  needle,  /f ,  therefore  the  displacements 
of  the  stirrup  itself  amount  in  these  cases  only  to  0.033  and 
0.025  mm.  After  frequent  repetition  of  the  experiment,  by 
which  the  ligaments  were  thoroughly  stretched,  the  amplitude 
of  displacement  increased  to  0.050  mm.  In  another  preparation 
only  the  superior  semi-circular  canal  of  the  labyrinth  was  open- 
ed, according  to  Politzer's  plan,  from  the  upper  side  of  the  tem- 


I 


MECHANISM    OF   THE    OSSICLES   OF   THE   EAR.  43 

poral  bone.  Into  the  opening  tlins  made  Avas  inserted  a  slen- 
der glass  tnbe,  whose  transverse  section  was  found,  by  calibration 
with  quicksilver,  to  be  0.228  of  a  square  millimetre.  The  vesti- 
bule and  a  portion  of  the  tube  were  filled  with  water.* 

The  movements  of  the  bones  of  the  ear  produced  by  forcing 
air  into  the  external  meatus  caused  the  fluid  in  the  tube  to  rise 
0.9  mm.  Now,  since  the  diameters  of  the  fenestra  ovalis  were 
found  equal  to  1.2,  and  3  mm.,  therefore  the  surf  ace  of  the  fe- 
nestra ovalis  is  nearly  12.4  times  as  large  as  the  transverse  section 
of  the  glass  tube.  The  mean  amplitude  of  the  excursion  of  the 
base  of  the  stirrup  must  then  be  j-j^  of  that  of  the  fluid  in  the 
tube,  which  is  0.0726  mm.  According  to  the  highest  calcula- 
tion, the  excursions  of  the  stirrup  amount  to  y\  and  j\  mm. 

The  relation  of  the  stirrup  to  the  anvil  is  such  that  if  the 
handle  of  the  hammer  be  drawn  inward,  the  long  process  of 
the  anvil  presses  firmly  against  the  knob  of  the  stirrup ;  the 
same  takes  place  if  the  capsular  ligament  between  both  be  cut 
through. 

If  the  manubrium  be  moved  outward  as  far  as  the  ligaments 
of  the  hammer  will  allow,  then,  in  case  the  capsular  ligament  be 
cut,  the  long  process  of  the  anvil  will  recede  from  ^  to  ^  mm. 
from  the  stirrup.  "With  this  position  of  the  hammer,  if  the  han- 
dle of  the  anvil  be  pressed  back  against  the  stirrup,  it  will  re- 
main in  this  position  without  springing  back  ;  at  the  same  time 
the  cogs  of  the  joint  of  the  hammer  and  anvil  become  separated 
entirely,  and  there  is  no  force  present  sufficiently  powerful  to 
draw  the  anvil  back.  In  the  normal  condition  of  the  arti- 
culation of  the  anvil  and  stirrup,  the  })oint  of  the  handle  of 
the  anvil  remains  always  attached  to  the  stirrup;  but  it  follows, 
from  the  already-mentioned  facts,  that  the  anvil  exercises  no 
strain  upon  the  stirrup  when  the  handle  of  the  hammer  is  driven 

*  In  order  to  render  it  air-tight,  I  first  dried  the  bone  as  much  as  possible  witli 
blottino-paper  ;  then  I  applied  a  red-hot  iron  wire  to  the  margin  of  the  opening 
in  the  semi-circular  canal,  and  upon  this  spot  I  placed  immediately  a  drop  of  hot 
cement  made  of  wax  and  resin  ;  in  this  the  glass  tube  was  fastened.  Finally, 
the  preparation  was  set  in  a  bowl  of  water  of  sufficient  depth  to  cover  the  free 
end  of  the  glass  tube,  and  then  the  whole  was  placed  under  the  air-])ump.  On 
exhausting  the  air  in  the  chamber,  the  air  iu  the  vestibule  escaped  through  the 
tube,  and  then  water  took  its  place. 


44  MECHAJ^ISM   OF  THE   OSSICLES   OF   THE   EAR. 

outward,  since  tlie  handle  of  the  anvil,  even  when  the  articu- 
lation is  severed,  can  remain  in  contact  with  the  stirrup  with- 
out being  drawn  outward  with  the  handle  of  the  hammer. 

This  arrangement  has  this  important  result,  namely,  that  by 
means  of  an  increase  of  pressure  in  the  cavity  of  the  drum  or 
diminution  of  pressure  in  the  meatus,  the  membrana  tympani 
and  the  hammer  can  be  perceptibly  driven  outward  without  the 
stirrup  incurring  the  danger  of  being  torn  from  the  fenestra 
ovalis.  Tlie  membrana  tympani  serves  as  a  very  powerful  re- 
straint to  the  reverse  movement  of  the  hammer. 

Since  the  point  of  the  long  process  of  the  anvil,  seen  from  the 
axis-band,  is  inclined  still  further  backward  than  the  point  of 
the  handle  of  the  hammei',  therefore  the  former  rises  wlien  press- 
ed inward  more  than  the  latter,  and  the  elevation  is  not  entire- 
ly compensated  for  by  the  slight  depression  of  the  hammer  al- 
ready mentioned  ;  in  short,  the  driving  of  the  membrana  tym- 
pani inward  causes  the  point  of  the  head  of  the  hammer  to  be 
driven  outward  and  at  the  same  time  slightly  elevated. 

This  agrees  witli  the  corresponding  movement  of  the  tirrup, 
whose  knob-like  head  rises  slightly  when  the  stirrup  is  pressed 
inward  in  consequence  of  its  unequal  attachment  to  the  upper 
and  lower  border  of  the  fenestra  ovalis.  This  lever-like  move- 
ment has  already  been  observed  and  described  by  Ilenke,* 
Lucae,t  and  Politzer.ij:  In  reply  to  the  first,  I  will  only  remark 
that  the  lever-like  movement  of  the  stirrup  is  by  no  means  its 
only  one  ;  that  "  perhaps"  one  border  of  the  plate  of  the  stirrup 
is  not  moved  inward  while  the  other  moves  outward.  Look- 
ing at  the  base  of  the  stirrup  from  the  vestibule,  we  can  much 
more  easily  recognize  the  fact  that  both  borders  are  driven  out- 
ward and  inward  simultaneously  ;  the  superior,  however,  more 
than  the  inferior. 

The  apparent  discrepancies  between  the  observations  of 
Lucae  and  Politzer,  in  respect  to  the  effect  which  an  increased 
pressure  of  air  in  the  cavity  of  the  tympanum  has  upon  the 

*  Der  Meclianisinus  der  GehOrkiiuchelclien,  in  der  Zeitschrift  fur  rationelle 
Medicin.     1868. 
f  .\rcUiv  fiir  OhrenUeilkunde.     Vol.  iv.  pp.  36,  37. 
}  Woclienblatt  der  K.  K.  Gesellscliaft  der  Aerzte.     Wien,  1868. 


MECHANISM    OF   THE    OSSICLES    OF   THE    EAE. 


45 


stirrup  and  the  water  of  tlie  labyrintli,  are  to  be  explained  by 
supposing  that  Lucae  observed  the  lever-like  movement  of  the 
stirrup,  and  Politzer  the  oscillation  which  takes  place  in  the  wa- 
ter  of  the  labyrinth  when  tlie  stirrup  is  pressed  inward.  Neither 
is  it  always  necessarily  in  the  same  degree  ;  at  least  not 
in  this  case,  because  the  pressure  of  the  air  through  the  fenestra 
rotunda  can  also  cause  increased  pressure  in  the  labyrinth. 

§.6. 
The  Concerted  Action  of  the  Bones  of  the  Ear. 
If  we  suppose  the  hammer  and  anvil  so  united  that  their 
cogs  press  against  one  another  and  both  move  like  one  com- 
pact body,  exerting  a  pressure  upon  tlie  point  of  the  handle 
of  the  hammer,  which  is  continued  inward  and  transmitted 
from  the  anvil  upon  the  stirrup,  then  the  system  of  the  two 
ossicles  can  be  considered  as  a  one-armed  lever  whose  fulcrum 
lies  where  the  point  of  tlie  short  process  of  the  anvil  presses 
outward  against  the  wall  of  the  cavity  of  the  tympanum.  The 
tip  of  the  handle  of  the 
hammer  represents  the 
point  of  i^ressure,  and  the 
point  of  the  handle  of  the 
anvil  the  other  point  which 
resists  this  pressure.  These 
three  points  lie  in  fact  very 
nearly  in  a  straight  line,  so 
that  the  point  of  the  anvil 
and  stirrup  recedes  only 
very  slightly  inward  from 
the  straight  line  of  union 
between  the  tip  of  the  han- 
dle of  the  hammer  and  the 
outer  side  of  the  articula-  ^'S-  9- 

tion  of  the  anvil  with  the  tympanum.  This  can  easily  be  seen 
in  preparations  where  the  natural  union  of  the  bones  is  still  pre- 
served. Fig.  y.  represents  both  bones  in  tlie  position  where 
their  cogs  are  attached  to  one  another ;  a «  is  the  straight 
line  which  passes    through  the  three  points  mentioned  above ; 


46  MECHANISM    OF    THE   OSSICLES   OF  THE    EAR. 

P .  F.,  the  stmnp  of  the  processus  Foliaims;  T.t.  the  tendon  of 
the  tensor  tympani  ;  and  at  h  we  have  the  cog  of  the  anvil. 
In  this  ])reparation  I  found  the  entire  length  of  the  lever  to  be 
9^  mm.,  the  shorter  arm  between  the  two  points  of  the  anvil 
6J  mm.,  so  that  the  latter  is  f  of  the  length  of  the  longer  arm. 
Hence,  when  the  hanniier  and  anvil  lie  close  together,  the  excur- 
sion of  the  tip  of  the  handle  of  the  anvil  will  amount  only  to  f 
of  that  of  the  handle  of  the  hammer,  but  the  amount  of  the 
pressure  wliicli  tlie  former  exerts  upon  the  stirrup  will  be  1^ 
times  as  great  as  the  force  wliich  is  exerted  against  the  handle 
of  the  hammer. 

Since  the  three  points  of  the  lever  lie  in  a  straight  line,  there- 
fore the  pressure  is  quite  independent  of  the  position  of  the 
remaining  parts  of  the  ossicles — presupposing  only  that  tlie 
latter  maintain  a  position  in  which  the  articular  surfaces  press 
firmly  against  each  other. 

This  result  will  be  obtained  in  the  following  manner:  While 
the  membrana  tympani  is  being  driven  inward,  the  hammer 
will  rotate  about  an  axis  which  is  inclined  obliquely  (30°)  to- 
ward the  plane  of  insertion  of  the  memln'ana  tympani.  and  its 
head  will  recede  from  the  tympano-incudal  joint,  thus  putting 
the  malleo-incudal  capsular  ligament  on  the  stretch.  Now,  since 
every  attempt  to  rotate  the  ossicles  in  such  a  manner  that  the 
cogs  will  press  against  each  other,  produces  instantly  a  conside- 
rable separation  of  the  articular  surfaces,  therefore  the  already 
tense  fibres  of  the  capsular  ligament  serve  to  resist  any  force 
capable  of  producing  this  result.  On  the  other  hand,  if  the 
membrana  tympani  be  driven  outward,  the  capsular  ligament 
becomes  relaxed  and  yields  to  such  an  extent  as  to  allow  of  a 
slight  separation  of  the  articular  surfaces,  like  that  which 
happens  when  the  cogs  are  separated.  The  remaining  displace- 
ments, which  the  malleo-incudal  joint  admits  of,  do  not  cause 
the  above-mentioned  three  points  of  the  lever  to  depart  from 
the  straight  line.  One  of  the  axes  of  rotation  of  this  saddle- 
shaped  joint  passes  through  the  tip  of  the  handle  of  the  ham- 
mer ;  the  other  is  perpendicular  to  the  plane  which  passes  through 
the  three  points  and  tlie  articuhition,  and  consequently  sepa- 
rates the  long  process  of  the  anvil  from  the  handle  of  the  hammer. 


MECHANISM    OF    THE    OSSICLES   OF    THE   EAE.  47 

In  tlie  above-mentioned  experiments,  Avliere,  as  a  general  thing 
the  stirrup  has  been  set  in  motion  by  exerting  pressure  upon  the 
hammer  or  upon  tlie  membrana  tympani,  we  have  seen  that  tlie 
amplitude  of  the  excursion  becomes  sliglitlj  diminished,  that  is, 
to  about  f  of  its  magnitude.  In  order  to  determine  the  firm 
ness  of  the  mechanism  I  tried  the  reverse  experiment  and 
endeavored  to  measure  the  extent  of  the  excursion  of  the 
liammer  by  pressing  the  base  of  the  stirrup  outward  and  thus 
setting  the  liammer  in  motion.  In  this  case,  of  course,  the 
onl}' movements  of  the  hammer  to  be  taken  into  consideration 
are  those  which  cause  it  and  the  anvil  to  remain  in  close  con- 
tiguity at  the  point  of  contact.  (The  preparation  used  in  this 
experiment  has  been  already  described  as  having  a  tube  inserted 
into  the  vestibule.)  Having  cemented  a  glass  thread  59  mm. 
long  to  the  head  of  the  hammer,  I  endeavored  to  find  how 
mnch  motion  could  be  produced  in  the  hammer  by  alternately 
forcing  fluid  through  the  glass  tube  and  then  withdrawing  it 
from  the  same.  The  excursion  at  the  tip  of  the  glass  thread 
amounted  only  to  about  ^  mm.  If  4  mm.  be  the  distance 
from  the  axis  of  rotation  to  the  point  where  the  glass  thread 
is  fastened  to  the  head  of  the  hammer,  then  the  length  of  the 
lever  is  63  mm.  and  the  above-mentioned  excnrsion  of  ^  mm. 
corresponds  to  a  rotation  of  about  half  a  degree.  For  the  tip  of 
the  handle  of  the  liammer,  whose  distance  from  the  axis-band 
amounts  to  4|-  mm.,  this  gives,  on  the  other  hand,  an  excursion 
of  only  2V  mm,,  an  amount  which  is  about  the  same  as  the 
mean  value  of  the  excursion  of  the  base  of  the  stirrup.  Tlieo- 
retically  we  should  expect  a  somewhat  greater  value  for  the 
excursion  of  the  handle  of  the  hammer.  Taking  into  consider- 
ation the  diminished  tension  of  animal  tissue  after  death,  and 
the  want  of  elasticity,  namely,  of  the  tensor  tympani,  we  cannot 
well  expect  in  the  nnited  action  of  the  bones  of  the  ear  the 
same  precision  which  we  find  in  the  living  subject.  In  this  way 
the  transmission  of  the  light  movements  of  the  anvil  to  the 
hammer  may  be  impaired.  * 

*  I  will  remark  in  this  connection  tliat  the  transmission  of  the  movements  of 
the  membrana  tympani  to  tlie  water  of  the  vestibule  was  also  perceptibly  im- 
paired at  the  time  when  I  made  the  above  described  experiment.     I  obtained 


48  MECHANISM    OF   THE    OSSICLES   OF  THE   EAR. 

Tliese  different  attempts  at'measurement  coincide  tlius  far  in 
showing  tliat  the  disph^cenients  of  the  stirrup  and  hannner,  as 
long  as  tlie  two  remain  tirmly  connected,  are  limited  to  ampli- 
tudes each  of  which  is  smaller  than  a  tenth  part  of  a  millimetre. 

On  tlie  other  hand,  if  we  put  the  hammer  in  motion  by 
forcing  air  into  the  external  meatus  and  then  withdrawing  it? 
the  glass  thread  attached  to  the  ossicle  indicates  much  greater 
excursions ;  its  point  moves  backward  and  forward  5  mm., 
while  before  (as  already  mentioned)  it  experienced,  in  a  direction 
from  the  stirrup  outward,  only  a  displacement  of  ^  mm. 

The  excursion  which  the  hammer  can  make  without  the  an- 
vil is  nearly  nine  times  as  great  as  that  which  the  two  together 
can  accomplish.  This  kind  of  movement  is  not  transmitted  to 
the  water  of  the  lal)yrinth,  excepting  of  course  the  slight  changes 
in  pressure  which  the  changed  tension  of  the  articular  liga- 
ments, or  the  rubbing  of  the  articular  surfaces  of  the  malleo- 
incudal  joint  upon  one  another,  are  perhaps  sufficient  to  pro- 
duce in  the  water  of  the  labyrinth  when  the  cogs  of  the  articu- 
lation are  no  longer  in  contact.  If  you  force  air  into  the  ca- 
vity of  the  tympanum  of  your  own  ear,  you  will  hear  feeble 
tones  issuing  from  the  middle  and  upper  portions  of  the  scala, 
almost  if  not  quite  as  distinctly  as  usual ;  on  the  other  hand,  it 
is  very  apparent  that  we  hear  the  same  tones,  when  they  are 
given  forcibly,  much  more  distinctly  when  the  pressure  in  the 
cavity  of  the  tympanum  is  uniform  than  when  it  is  increased. 
This,  I  think,  shows  that  the  articular  surfaces  of  the  hammer 
and  anvil  can  adhere  together  and  be  firmly  united  by  means 
of  motion  on  one  another,  similar  to  that  which  takes  place  in 
anatomical  preparations  when  the  joint  of  the  anvil  and  stirrup 
lias  been  cut  through  aiid  the  rarefaction  of  the  air  in  the  mea- 
tus auditorius  has  caused  the  liammer  to  be  drawn  outward. 
The  anvil  then  is  also  drawn  outward ;  but  if  we  turn  it  by 
means  of  a  needle,  so  that  its  long  process  again  touches  the 
stirrup,  it  M'ill,  as  mentioned  above,  still  remain  fixed  in  this 

only  0.4  mm.  ele\ation  in  the  manometer,  whereas,  on  the  day  before,  when  I 
had  filled  the  vestibule  with  water  under  the  air-pump,  the  elevation  amount- 
ed to  0.9  mm.  It  is  to  be  hoped  that  some  anatomist,  who  has  an  abundance 
of  suitable  preparations  at  his  command,  will  repeat  these  experiments.  Of 
course  the  specimens  should  be  as  fresh  as  possible. 


MECHANISM    OF    THE    OSSICLES    OF   THE   EAR.  49 

position.  Friction  will  also  cause  tlie  anvil  to  adhere  iirnily  to 
the  hammer  in  the  position  already  given,  in  opposition  to  the 
tension  of  the  ligaments  or  any  other  mild  forces,  and  that  too 
when  the  vibrations  of  sonnds  are  feeble.  More  powerful  forces 
or  concussions  will  of  necessity  cause  the  two  bones  to  slide 
upon  one  another,  and  strong  vibrations  of  sound  in  such  a  posi- 
tion of  the  bones  will  be  very  percejjtible. 

I  have  used  in  these  experiments  a  watch  and  a  tuning-fork ; 
striking  the  latter  lightly,  I  held  it  so  far  from  the  ear 
that  the  beats,  which  the  rotation  of  the  fork  upon  its  long 
axis  produced,  were  still  perceptible.  We  hear  them  just  as 
distinctly  when  the  membrana  tympani  is  distended,  provided 
they  belong  to  the  upper  octaves  of  the  scale,  and  very 
nearly  as  distinctly  in  the  middle  octaves.  The  deeper  tones 
are,  of  course,  considerably  weaker.  On  the  other  hand,  a  tun- 
ing-fork of  a  higher  pitch,  when  struck  forcibly  and  held  be- 
fore the  ear  while  the  membrana  tympani  was  distended, 
showed  a  very  perceptible  crescendo,  just  as  we  restored  the 
equilibrium  of  the  air  by  the  motion  of  swallowing. 

I  wish  to  call  attention,  in  this  connection,  to  another  pheno- 
menon whose  explanation,  I  think,  can  be  deduced  from  the 
mechanism  already  described.  If  we  take  a  tuning-fork  which 
consists  of  a  single  piece  of  steel,  and  which  therefore  has  noth- 
ing about  it  which  can  give  a  rattling  sound,  and,  after  having 
struck  it  forcibly,  hold  it  near  the  ear  so  that  the  sound  can  be 
heard  very  distinctly,  the  character  of  the  tone  becomes  sharp, 
and  we  hear  distinctly  jarring  sounds  similar  to  what  is  heard 
in  musical  instruments  when  something  is  loose,  or  from  a  tun- 
ing-fork when  pressed  rather  lightly  upon  a  sounding  board. 
These  iarrino;  sonnds  result  from  the  slight  shocks  which  a  vi- 
brating  body  makes  upon  a  body  at  rest  or  vibrating  in  a  diffe- 
rent manner.  These  blows  are  repeated  regularly  and  produce 
sound  ;  but  inasmuch  as  they  correspond  to  an  interrupted  pe- 
riodical movement,  the  sound  possesses  very  many  overtones 
and  is  harsh  in  character.  Such  tones  occur,  as  is  well  known, 
in  the  ear  itself  as  the  result  ot  very  loud  sounds.  We  can  hear 
also  from  a  B  tuning-fork  of  116  vibrations  a  jarring  sound  so 
distinctly  that  it  resembles  a  buzzing  in  the  ear.  This  jarring 
4 


50  MECHANISM    OF   THE   OSSICI,ES    OF    THE    EAR. 

tone  is  very  distinct  and  strong  when  the  pressure  of  the  air  in 
the  cavity  of  the  tympanum  is  equal  to  or  less  than  that  of  the 
atmosphere,  and  when  the  cogs  of  the  hammer  and  anvil  are 
closely  united;  but  it  disappears  when  the  air  is  driven  into  the 
cavity  of  the  tympanum  and  the  cogs  are  consequently  sepa- 
rated. I  think,  therefore,  that  we  are  justified  in  concluding 
that  this  jarring  tone  is  caused  by  the  cogs. 

When  tlie  excursions  of  the  membrana  tympani  are  very 
great,  and  during  the  outward  phase  of  the  vibration,  the  anvil 
is  not  driven  outward  with  any  considerable  force,  and  cannot 
therefore  follow  perfectly  the  excursions  of  the  hammer ;  the 
result  of  wliich  is  that  they  are  separated,  and  that  during  the 
next  vibration  inward  the  anvil  receives  a  blow  from  the  re- 
turning hammer.  This  mechanism  is  also  well  adapted  to  the 
production  of  combination  tones,*  and  the  peculiar  sensation  of 
buzzing  in  the  ear  resulting  from  tlie  combination  tones  of  two 
strong  soprano  voices,  when  thirds  are  sung,  can,  I  think,  be  re- 
ferred to  this  jarring  which  takes  place  between  the  hammer 
and  anvil. 

This  phenomenon  is  also  of  great  importance  in  its  relation 
to  the  sensation  which  liarmony  produces  in  the  ear,  since  strong 
tones  whieli  take  place  outside  of  the  ear,  and  without  over- 
tones, must  of  necessity  develop  liarmonious  overtones  in  the 
ear.  In  this  way  sounds  with  harmonious  overtones,  which 
correspond  to  a  regular  periodical  movement  of  the  air,  acquire 
a  natural  preference  over  those  with  unliarmonious  overtones, 
especially  as  the  whole  doctrine  of  conferences  becomes,  through 
this  circumstance,  independent  of  the  overtones  connected  with 
external  sound.  The  jarring  tones  can  be  much  deeper  than 
the  exciting  tone,  if  the  vibrating  body  falls  back  only  after  the 
expiration  of  the  vibrations,  and  hence  receives  another  blow. 

To  this  class,  I  believe,  belong  also  certain  deep,  harsh  sounds 
which  we  liear  when  the  shrill  high  notes  of  the  upper  octave 
(a^  —  g^)  are  sounded  very  distinctly.  It  is  probable  that  an 
unusually  strong  vibration  is  produced  at  the  same  time  in  the 
surface  of  the  membrana  tympani,  judging  from  a  certain  buz- 
zing, tickling  sensation  which  is  felt  in  the  deep  parts  of  the 
*  VideLebre  von  den  Tonempfindungen,  pages  233-236. 


MECHANISM    OF   THE    OSSICLES   OF   THE    EAR.  51 

ear.     The  apparatus  described  further  on  (Fig.  11)  is  particularly 
adapted  to  the  production  of  such  tones, 

I  will  mention  here  that  I  have  made  an  enlarged  model  of 
the  apparatus  of  the  cavity  of  the  drum,  in  order  to  prove  the 
comi3leteness  and  correctness  of  the  explanation  just  given. 
The  bones  of  the  ear  are  made  of  wood,  the  membrana  tym- 
pani  of  glove-leather,  cut  in  such  a  way  that  a  seam  shall  run 
along  the  handle  of  the  hammer  where  the  leather  is  attached 
to  that  ossicle.  By  this  means  we  can  give  to  it  its  conical 
form.  An  opening  of  suitable  form,  cut  in  a  board,  and  having 
beveled  edges  to  which  the  edges  of  the  artificial  membrana 
tympani  are  fastened,  represents  the  inner  end  of  the  external 
meatus.  On  the  outside  of  the  board  a  tin  ring  is  fastened,, 
which  surrounds  the  already  mentioned  opening.  To  this,, 
finally,  a  tin  cover  having  a  gutta-percha  edge  is  fitted,  like  the 
covers  of  hermetically  sealed  fruit-jars.  Now,  if  we  place  this 
cover  so  that  a  portion  of  the  gutta-percha  rim  remains  be- 
tween it  and  the  tin  ring,  condensation  of  the  air  may  be  pro- 
duced on  the  outer  side  of  the  artificial  membrana  tympani, 
which  will  act  upon  the  bones  of  the  ear. 

On  the  inside,  near  the  upper  and  anterior  edge  of  the  open- 
ing, a  thin  piece  of  wood  with  a  projecting  point  is  fastened, 
which  latter  represents  the  spina  tympanica  major.  A  hemp 
string,  which  is  attached  to  the  latter,  penetrates  the  hammer 
and  passes  around  it,  then  passes  through  the  board  at  the  pos- 
terior superior  edge  of  the  opening.  This  string,  which  is  intend- 
ed to  represent  the  axis-band,  can  be  rendered  tense  by  an  ordina- 
ry screw-eye.  The  tendons  of  the  ligamentum  externum  and  the 
ligamentum  anterius  mallei,  which  pass  from  the  spina  upward,, 
can  be  represented  by  other  strings,  which  of  course  must  be  ac 
curately  applied  and  provided  with  screw-eyes  to  vary  their 
tension.  Finally,  the  tendon  of  the  tensor  tympani  can  be  re- 
presented by  a  silk  thread  which  passes  through  an  iron  ring 
made  fast  to  a  small  wooden  pillar,  and  then  is  connected  with 
a  tense  gatta-percha  band.  I  first  spread  warm  sealing-wax 
upon  the  articular  surf  ace  of  the  hammer,  and  endeavored  as  far 
as  possiI)le  to  give  to  the  former,  before  it  had  grown  cold,  the 
corresponding  form  ;  then  I  laid  soft,  hot  sealing-wax  upon  the 


52  MECHANISM   OF  THE   OSSICLES   OF  THE   EAR. 

articular  surface  of  the  anvil,  and,  after  having  covered  the  articu- 
lar surfiice  of  the  hammer  with  tin-foil,  I  pressed  the  two  to- 
gether, Tlie  tin-foil  then  adheres  to  the  anvil.  Now,  before  the 
sealing-wax  had  become  quite  cold,  I  made  a  twisting  movement 
witli  the  anvil,  similar  totliat  which  occurs  between  these  bones 
in  the  ear,  in  order  to  render  these  surfaces  capable  of  sliding 
upon  one  another.  After  the  articular  surface  of  the  anvil  had 
become  cold,  it  served  as  a  form  upon  which  to  mould  the  sur- 
face of  the  hammer  (which  must  be  heated  and  covered  with 
tin-loil)  and  render  it  capable  of  gliding  over  the  articular  sur- 
face of  the  anvil.  This  experiment  was  repeated  alternately 
with  one  and  the  other  articular  surfece  until  the  two  moved 
sufficiently  easily  upon  one  another.  It  was,  of  course,  neces- 
sary not  to  make  any  sliding  movements  strong  enough  to  dis- 
turb the  cogs.  In  this  way  I  succeeded  finally  in  obtaining  a 
good  articulation.  The  capsular  ligament  was  constructed  of 
loops  of  thin  elastic  India-rubber  cord,  which  were  fastened  to 
the  anvil  and  could  be  drawn  over  and  attached  to  the  hammer 
by  means  of  small  hooks  made  of  pins,  thus  holding  the  two 
hones  together  by  a  very  slight  elastic  pressure. 

The  articular  ligament  of  the  short  process  of  the  anvil  was 
represented  by  a  loop  of  silk  threads  which  passed  through  a 
hole  in  the  anvil.  This  band  can  be  loose,  but  it  is  of  impor- 
tance that  the  point  of  support  of  this  part  of  the  anvil  upon  the 
outer  wall  of  the  cavity  of  the  drum  should  be  represented  in 
the  model. 

Simple  contact  is  sufficient  to  represent  the  union  between 
the  long  process  of  the  anvil  and  the  stirrup,  or  a  loop  of  silk 
threads  can  be  employed.  The  former  is  quite  sufficient  for 
giving  direction  to  the  blows  above  described. 

The  fenestra  ovalis  was  cut  in  a  thin  piece  of  board,  which 
was  held  parallel  to  the  larger  board  by  means  of  small  wood- 
en pillars.  This  hoard  consisted  of  two  plates  screwed  together, 
between  which  was  a  thin  layer  of  gutta-percha,  representing 
the  membrane  of  the  fenestra  ovalis.  The  foot-plate  of  the 
artificial  stirrup  was  likewise  double  and  had  an  interposed 
layer  of  India-rubber,  and  the  whole  was  fastened  together  by 
screws. 


MECHANISM   OF   THE   OSSICLES   OF   THE    EAR.  63 

Such  a  model  is  very  useful,  partly  in  demonstrations  and 
partly  to  show  clearly  what  part  the  individual  ligaments  and 
also  the  articulations  play  in  connection  with  the  attachment 
of  the  bones  of  the  ear ;  for  all  these  different  parts  can  be  se- 
parated, and  each  ligament  can  be  made  tighter  or  looser. 
Moreover,  this  model  transmits  with  great  facility  to  the  stirrup 
the  small  blows  which  are  directed  on  the  outside,  immediately 
upon  tlie  manubrium  or  upon  the  already  mentioned  air-tight 
cover ;  this  can  be  felt  when  the  linger  is  placed  over  the  base 
of  the  stirrup  and  over  the  plate  in  wdiich  it  rests,  and  is  also 
recognizable  in  the  bounding  up  of  light  bodies  which  have 
been  laid  upon  it. 

The  diameters  of  the  artificial  membrana  tympani  are  80  and 
120  mm.  The  remaining  parts  are  constructed  according  to 
this  measurement.  All  the  statements  contained  in  the  foregoing 
description,  in  regard  to  the  mobility  and  mode  of  attachment 
of  the  parts,  I  have  tested  and  found  confirmed  in  this  model. 

Mechanism  of  the  Menibrana  Tympani. 

The  membrana  tympani  is  to  be  considered  as  a  tense  mem- 
brane, which,  however,  ditiers  essentially  from  those  which 
have  been  hitherto  studied  in  acoustics,  in  the  fact  that  it  is 
curved.  Its  tension  is  modified  by  the  handle  of  the  liammer 
which  draws  it  inward,  and  which  is  itself  retained  in  tliis 
position  by  means  of  ligaments  of  attachment,  and  by  the  elas- 
ticity of  the  tensor  tympani.  If  the  radial  fibres  of  the  mem- 
brana tympani  were  not  united  by  transverse  ones,  they  would 
be  stretched  in  a  straight  line.  In  point  of  fact,  however,  tliey 
maintain  a  curved  shape  with  the  convexity  looking  toward 
the  meatus ;  hence  we  conclude  that  the  radial  fibres  are  drawn 
toward  one  another  by  circular  fibres,  and  that  the  latter  are 
also  made  tense  at  the  same  time.  There  is,  in  fact,  in  the  mem- 
brana tympani  at  rest  no  other  force  capable  of  holding  the 
radial  fibres  in  a  curved  position,  except  tlie  tension  of  tlie 
circular  fibres. 

In  the  concussions  which  sound  produces,  the  pressure  of  the 
air  acts  sometimes  upon  the  convex,  sometimes  upon  the  con- 


54  MECHANISM    OF   THE   OSSICLES   OF   THE   EAE. 

cave  siirfiice  of  tlie  inerabrana  tympani,  according  as  tliis  pres- 
sure is  alternately  greater  or  less  in  the  meatus  thaii  in  the 
cavity  of  the  tympani ;  in  every  case  the  pressure  of  the  air 
acts  perpendicularly  upon  the  membrane,  also  perpendicularly 
upon  the  curve  formed  by  the  radial  fibres,  which  curve  it  at 
one  time  increases  and  at  another  diminishes.  Since  the 
curves  formed  by  the  radial  fibres  of  the  membrana  tympani 
are  only  slight,  therefore,  as  will  bo  shown  afterward,  the 
mechanical  operation  is  the  same  as  if  the  pressure  of  the  air 
were  exerted  at  the  end  of  a  very  long  lever-arm,  while  the  tip 
of  the  manubrium  represents  the  end  of  a  very  short  lever-arm. 
A  relatively  great  displacement  of  the  surface  of  the  mem- 
brana tympani  in  the  same  direction  as  the  pressure  of  the  air 
necessitates  a  comparatively  small  displacement  of  the  point  of 
the  hammer,  and  vice  versa.  Hence,  in  accordance  Avith  the 
well-known  law  of  virtual  velocities,  a  relatively  sniall  amount 
of  pressure  of  the  air  wnll  counterbalance  a  comparatively 
strons:  force  actini>;  at  the  handle  of  the  hammer — in  other 
words,  it  will  supply  an  equivalent  force. 

In  order  to  understand  this,  we  can  limit  ourselves  to  the 
examination  of  a  single  curved  radial  fibre,  which  we  can  su])- 
pose  changed  by  the  pressure  of  the  air  into  circular  arcs  of 
constant  lengths  but  of  differing  curves,  and  hence  having 
differing  radii.  If,  then,  I  represents  the  length  of  the  fibre, 
r  the  radius  of  the  circle  to  wliich  the  arc  belongs,  and  A  the 

1     /L 

chord  which  belongs  to  the  arc  I,  then  is  -^j-  -^  the  sine  of  half 

of  the  angle  at  the  centre,  which  belongs  to  the  curve  I ;  there- 
fore, 

Z  =  2  r.  Arc.  sinf  n".) 
or 

and  the  difference  between  the  chord  and  the  curve 


'-^=^Hi  -  ^^"Qf 


Now,  if  the  curve  is  very  slight — that  is,  r  xery  large  compar- 
ed with  I — then  we  can  suppose  the  sine  of  this  formula  devel- 


MECHANISM    OF   THE   OSSICLES   OF   THE   EAR.  55 

oped  according  to  the  involution  of  its  arc,  and  limit  onrselves 
to  tlie  first  of  the  two  divisions  of  this  development,  since  the 
divisions  become  small  ru])idl)\ 

^'"    K2r)   =  27-  -  6  •  (sT-)  . 
This  gives 

1     P  i 

l-^=  ~  -, 1. 

24    r-  ) 

The  degree  of  curvature  of  the  are,  or  the  distance  s  of  its 
centre  from  the  centre  of  the  chord,  is  given  by  the  equation 
r  -  s  fl\ 

—    cos    (  —  ) 

or 

If  we  make  here  the  progressive  evolution  for  the  cosine,  we 
have 

'=^^ ■■•■h 


or,  eliminating  ?'  from  1  and  2, 
i  -  A  _  -  _ 

!Now,  the  difference  Z —A  represents  the  shortening  of  the 
chord  which  is  caused  by  the  increase  in  the  curve  of  the  arc, 
or  the  extent  to  which  the  two  ends  of  the  fibre  are  drawn  to- 
gether. On  the  other  hand,  s  is  the  displacement  of  the  middle 
of  the  fibre.  If,  now,  s  be  infinitely  small  in  comparison  Avith  I, 
the  length  of  the  fibre,  therefore  the  magnitude  l  —  X  in  the  last 
formula  is  an  infinitely  small  magnitude  of  the  second  order 
in  comparison  with  s.  The  reverse  is  clear,  namely,  if  we  may 
be  permitted  to  consider  the  fibre  as  inextensible,  the  very  small 
lengtliening  of  the  fibre  to  the  amount  Z —A  cannot  happen 
in  any  other  way  except  that  the  fibre  becomes  straightened 
and  its  centre  experiences  the  relatively  much  greater  displace- 
ment 8. 

On  the  other  hand,  in  respect  to  the  estimation  of  the  rela- 
tion of  forces,  there  is  a  well-known  formula  in  mechanics,  that 


56  MECHANISM   OF   THE   OSSICLES   OF    THE    EAR. 

the  tension  t  of  the  fibres,  if  p  represents  the  pressure  upon  its 
unit  of  length,  is  represented  by  the  following  equation : 

t  —  ip  r. 
The  correctness  of  this  formula  can  be  most  easily  understood 
when  we  suj^pose  each  fibre  everywhere  (from  end  to  end) 
equally  curved  and  perfectly  parallel  to  its  similarly  curved 
neighbors,  and  in  this  way  lengthened  to  a  half  circle.  Then 
the  forces  which  draw  upon  the  two  ends  of  the  fibre — that  is, 
2  t — must  counterbalance  the  pressure  which  acts  upon  the 
whole  diameter  of  the  semi-circle  throughout  a  width  equal  to 
that  of  the  fibre — that  is,  the  amount  2  /'.  j9  ;  and  hence  the  cor- 
responding equation 

3  i  =  2  7-  p. 

Therefore  the  greater  r  is,  tliat  is  to  say,  the  less  the  curve  is 
under  the  operation  of  the  pressure  of  the  air,  the  greater  will 
be  the  change  in  the  tension  produced  in  the  fibre  by  the  pres- 
sure of  the  air. 

These  changes  in  the  amount  of  tension  of  the  radial  fibres 
of  the  membrana  tyrapani  are  the  very  ones,  however,  which 
the  concussions  of  sound  transmit  to  the  handle  of  the  hammer. 
The  amount  of  tension  can  increase  very  considerably  under 
the  influence  of  comparatively  slight  changes  in  the  pressure  of 
the  air,  even  when  the  radial  fibres  of  the  membrane  are  stretch- 
ed out  in  a  very  flat  curve.  It  is  self-evident  that  in  propor- 
tion as  the  action  of  this  force  increases,  so  the  excursions  of 
the  handle  of  the  hammer,  which  can  be  caused  by  this  force, 
grow  smaller,  similarly  to  that  which  happens  when  the  inten- 
sity of  a  force  is  increased  by  means  of  a  lever. 

On  the  other  hand,  it  is  to  be  remarked  that  the  changes  in 
tension  wdiich  the  pressure  of  the  air  induces,  can  always  ap- 
pear as  the  increase  or  diminution  of  the  tension  which  is 
maintained  by  means  of  the  elastic  attachments  of  the  mem- 
brana tyrnpani  and  the  elasticity  of  its  own  radial  fibres.  A 
considerable  increase  in  tension,  through  the  pressure  of  the 
air  from  within  outward,  can  only  produce  a  slight  eflect  upon 
the  stirrup,  because  the  articulation  of  the  hammer  and  anvil 
yields.  Again,  on  the  other  hand,  the  pressure  of  the  air  from 
without  can,  at  the  most,  only  force  the  handle  of  the  hammer 


MECHANISM   OF   THE    OSSICLES   OF   THE    EAR.  57 

inward  until  tlie  radial  fibres  of  the  menibrana  tynipani  be- 
come straight;  should  the  pressure  be  still  greater,  tlien  it 
would  curve  them  again,  shorten  their  chord,  and  draw  tlie 
manubrium  again  outward,  provided  the  circular  fibres  of  the 
membrana  tymi^ani  could  actually  yield  so  much  without 
breaking,  which  latter  I  consider  very  improbable. 

The  labyrinth  is  likewise  protected  from  extremes  of  pressure, 
while  at  the  same  time  the  effect  of  slight  variations  in  pressure 
can  be  rendered  extremely  powerful  through  the  peculiarities 
of  the  mechanism  already  described. 

By  introducing  a  manometer  into  the  external  meatus,  ac- 
cording to  the  plan  proposed  by  Politzer,  it  may  be  shown  that 
the  excursion  of  the  parts  of  the  membrana  tympani  situated 
in  the  middle,  between  the  handle  of  the  hammer  and  the  bord- 
er of  attachment,  is  considerably  greater  than  that  of  the  ma- 
nubrium itself.  In  the  ordinary  anatomical  preparations  I 
found  it  better  to  fill  the  meatus  entirely  with  water  than  to 
shut  up  the  air  contained  in  the  meatus  by  means  of  a  drop  of 
water  in  the  tube  of  the  manometer.  A  drop  of  water  so  plac- 
ed resists  small  displacing  forces,  since  it  adheres  to  the  glass 
tube  and  does  not  move  when  most  desirable.  If  we,  however, 
fill  the  entire  meatus  with  water,  and  then  introduce  the  mano- 
meter-tube (after  having  attached  to  it  a  suitable  plug  of  seal- 
ing-wax) in  such  a  manner  that  at  the  same  time  a  certain 
amoimt  of  water  will  enter  it,  then  the  surface  of  the  fluid  in 
the  tube  will  indicate  very  accurately  the  displacements  of  the 
membrana  tympani.  As  already  mentioned,  a  tube  was  intro- 
duced into  the  vestibule  of  the  labyrinth  in  the  same  prepara- 
tion, and  thus,  by  forcing  in  the  fluid  or  withdrawing  it,  the 
stirrup  and  the  hammer  could  be  moved. 

It  has  already  been  stated  that  in  tliis  experiment  the  excur- 
sion of  the  tip  of  the  handle  of  the  hammer  was  only  ^\-  mm.  The 
height  of  the  fluid,  however,  in  the  manometer  varied  1  mm. 
By  calibration  with  quicksilver,  the  inside  diameter  of  the  tube 
was  found  to  be  1.37  mm. ;  the  diameters  of  the  membrana 
tympani  were  7^  and  9  mm.  From  this  we  can  calculate  a 
mean  displacement  of  the  membrana  tympani  of  somewhat 
more  than  ^  mm.  ;  that  is,  3  times  as  great  as  the  synchronous 


58  MECHANISM   OF  THE   OSSICLES  OF  THE   EAR. 

iriovement  of  tlie  tip  of  inanubriuni.  Now  since  the  outside 
border  of  the  ineinbrana  tympani  is  firm,  it  follows  that  the 
middle  free  parts  of  the  membrane  must  have  experienced  a 
relatively  much  greater  displacement  than  the  amount  of  the 
mean  displacement  given  above  and  therefore  more  than  three 
times  stronger  than  the  tip  of  the  handle  of  the  hammer. 

In  the  foregoing  elementary  examination  of  this  mechanism 
we  have  not  taken  into  consideration  the  following  facts,  viz.  : 
that  the  respective  meridional  curves  of  the  membrana  tympani 
are  closely  united ;  that  their  distance  from  one  another 
increases  in  the  direction  of  the  firm  border  of  the  membrane  ; 
that  they  are  bound  together  by  circular  fibres,  and  that  they 
cannot  move  without  stretching  these  ;  in  fact,  that  the  natural- 
ly curved  form  of  the  membrana  tympani  cannot  exist  without 
its  circular  fibres  being  extended  and  made  tense  by  every  force 
which  draws  the  handle  of  the  hammer  inward. 

The  form  of  the  membrana  tympani  being  so  irregular,  a 
perfect  analysis  of  the  mechanical  action  of  the  parts  cannot  be 
given.  It  would  be  necessary  first  to  know  the  tension  and  the 
measure  of  the  elasti(;ity  of  the  circular  fibres.  We  can,  how- 
ever, make  a  nuithcmatical  representation  which  would  better 
correspond  to  the  actual  relation  of  the  parts,  if,  instead  of  the 
real  membrana  tympani,  we  imagine  an  ideal  one,  which  is 
conical  in  the  centre,  but  toward  the  periphery  is  curved 
and  symmetrical,  and  represents  therefore  a  surface  of  ro- 
tation. The  radial  fibres,  which  follow  the  direction  of 
the  meridians  of  such  a  surface,  can  be  considered  as  incapable 
of  extension  ;  the  circular  fibres,  however,  must  possess  a  certain 
degree  of  elasticity  in  order  to  remain  always  tense.  In  the 
appendix,  I  have  developed  the  theoretical  question  regarding 
the  mechanical  workings  of  such  a  membrane,  and  the  most 
advantageous  form  to  give  it.  It  will  be  sufficient  here  to  remark 
that  the  pressure  of  the  air  will  produce  the  strongest  effect 
upon  a  slightly  curved  membrane,  when  it  has,  by  means  of  its 
own  elasticity,  taken  the  form  which  the  pressure  of  the  air  tends 
to  give  it.  This  form  is  one  where  with  unchanged  length  of 
the  radial  fibres  and  unchanged  position  of  its  centre,  the  volume 
of  its  concave  side,  that  is,  the  volume  of  the  cavity  of  the 


MECHANISM   OF  THE    OSSICLES    OF   THE   EAR. 


59 


drum  becomes  a  maxiinum,  and  tliat  on  its  convex  side  is  re- 
duced to  a  minimum.  If  the  membrane  had  not  originally 
possessed  such  a  form,  still  the  pressure  of  the  air  would  have 
produced  such  a  result  by  changing  the  tension  of  the  circular 
fibres,  before  it  could  have  excited  its  entire  force  upon  the 
centre. 

The  form  here  required  of  a  circular  membrane,  can  be  calcu- 
lated— the  transverse  section  of  such  an  one,  in  some  degree  cor- 
responding to  the  relation  of  the  membrana  tympani,  is  given 
in  Fiii'.  10.     This  form  will  be  seen  to  coincide  well  with  the 


relatively  free  lower  portion  of  the  membrana  tympani. 

Let  a  represent  the  angle  which  the  tangent  of  the  membraTie 
drawn  through  its  apex  (umbo)  in  the  meridian-plane  makes  av ith 
the  axis;  /3,  that  which  the  corresponding  tangent  of  a  point  in 
the  periphery  of  the  membrane  makes  with  the  axis  ;  B^  the  ra- 
dius of  the  circle  at  the  periphery  ;  /,  the  pressure  of  the  air  ; 
then  will  k  be  the  force  which  must  be  applied  at  the  centre 
of  the  membrane  to  counterbalance  the  pressure  of  the  air  : — 

_  P"^  ^'  ^^^  ® 


cos  a  —  cos  (3  ' 


In  this  equation  we  see  once  more  that  the  smaller  the  differ- 
ence between  the  two  angles  a  and  /3,  that  is,  the  shallower  tlio 
curve  made  by  the  the  tense  radial  fibres  of  the  membrane,  tho 


60 


MECHANISM   OF   THE    OSSICLES   OF   THE   EAR. 


stronger  will  be  the  force.  Further,  the  force  increases  as  tlie 
cos  a,  if  the  angles  a  and  jQ  become  smaller,  while  the  difference 
cos  a  —  cos  13  remains  the  same,  that  is,  if  the  apex  of  the  mem- 
brane be  drawn  in  more  strongly. 

Thus  far  the  acoustic  action  of  such  curved  membranes  has 
not  yet  been  practically  studied.  It  may  be  proper  to  state 
here,  that  in  the  Tunis  Cafe  at  the  Paris  industrial  exhibition, 
I  saw  a  curved  piece  of  leather  employed  as  a  sounding  board 
in  an  Arabian  stringed  instrument.  A  membrane  similar  to 
the  membrana  tympani  can  be  made  by  stretching  a  wet  piece 
of  a  pig's  bladder  over  the  upper  end  of  a  glass  cylinder :  the 
cylinder  should  be  placed  in  an  upright  position,  then  place 
a  rod  loaded  with  metal  perpendicularly  to  the  centre  of  the 
membrane,  so  that  its  lower  end  presses  the  centre  of  the  blad- 
der downward.  In  this  position  the  bladder  must  be  allowed 
to  dry.  It  will  then  retain  permanently  a  form  similar  to  that 
of  the  membrana  tympani,  with  its  retracted  navel  and  its  curved 
meridian  lines  whose  convexity  looks  outward. 

In  order  to  test  the  acoustic  action  of  such  a  membrane  under 
relations  similar  to  those  in  which  the  membrana  tympani  is 
placed,  I  fastened  the  cylinder,  whose  inside  diauieter  amounts 
to  44  mm.,  to  a  strong  wooden  board  (A,  Fig.  11.)  (In  the 
figure  the  cylinder  is  situated  between  e  and/",  and  has  been 


Jj 

jt 

iJ 

A 

a 

0? 

c 

J. 

H — ^ 

<P 

A 

f 

d 

6 

Fig.  11.  -si 

represented  as  cut  in  two.  The  cylinder  was  then  tied  to  the 
board,  its  open  end  at  6,  having  iirst  been  supported  by  a  piece 
of  wood,  properly  cut  out  to  receive  it,  by  which  arrangement 


MECHANISM   OF  THE   OSSICLES   OF   THE   EAR.  61 

any  sliding  movement  in  the  direction  of  e  was  prevented.  A 
small,  light  wooden  rod  was  then  placed  upon  the  retracted 
centre  of  the  membrane  and  this  served  as  a  bridge  for  a  string 
stretched  between  two  pegs  at  a  and  h.  At  c  the  string  runs 
over  a  bridge  placed  on  the  centre  of  a  block  of  lead,  be_yond 
which,  of  course,  the  string  cannot  vibrate.  Another  block  of 
lead  was  placed  at  fZ,  and  between  it  and  the  rod/",  a  thin  board 
like  the  bridge  of  a  violin  was  inserted  parallel  to  the  string.  This 
board  supported  the  rod,  but  offered  no  obstruction  to  the  shocks 
which  the  rod  received  in  the  direction  of  its  own  length,  from 
the  string. 

The  blocks  of  lead  serve  to  weaken  the  transmission  of  the 
vibration  of  the  string  to  the  board  and  so  through  it  to  the 
atmosphere,  so  that  when  we  draw  a  violin  bow  across  tlie  string 
and  at  the  same  time  lift  up  the  rod/"  from  the  curved  mem- 
brane, or  grasp  the  string  with  the  lingers  at  a  point  near/",  be- 
tween this  point  and  c  the  resulting  sound  will  be  very  much 
muffled.  As  soon,  however,  as  the  vibrations  of  the  string  can 
pass  through  the  rod  to  the  curved  membrane,  the  latter,  not- 
withstanding its  suddeness,  gives  forth  almost  as  powerful  a 
tone  as  the  violin  itself.  The  string  can  easily  be  shortened  by 
holding  it  between  two  fingers  of  the  left  hand,  while  with  the 
right  hand  we  draw  the  bow,  which  should  be  placed  near  the 
fingers  of  the  left  hand.  It  is  evident  then,  that  this  powerful 
resonance  extends  over  the  greater  portion  of  the  scale,  and  in 
the  case  of  the  high  tones  in  the  middle  of  the  octave  c^  .  .  c^ 
it  reaches  such  an  intensity  that  they  can  hardly  be  endured. 

This  process  resembles  that  which  takes  place  in  the  membrana 
tympani,  in  so  far  as  the  curved  membrane  serves  to  transmit 
the  vibrations  from  the  air  to  a  solid  body  of  moderate  weight 
and  relatively  small  amplitude  of  vibration,  as  for  instance 
the  labyrintli-water  on  the  one  hand,  and  the  ends  of  the 
strings  on  the  other.  If,  however,  sound  be  easily  transmitted 
from  the  string  to  the  air,  then  the  reverse  must  also  easily  take 
place,  according  to  the  general  law  of  reciprocal  forces  for  oscil- 
lations of  sound  in  perfectly  elastic  bodies.' 

'  The  law  for  masses  of  air  inclosed  in  firm  walls  is  stated  and  proven  in  an 
essay  published  by  me  in  the  "Journal  fiir  reine  and  an^rewandtc  Matliematik." 
Bd.  LVII.  p.  29.  Equation  93.  The  title  is, "  Theorie  der  Luftschwingungen 
in  Rohren  niit  offenen  Enden." 


62  MECHANISM    OF   THE    OSSICLES   OF   THE    EAR.  ' 

I. 

Tlic  proof  of  tins  can  easily  be  found  by  experiment  on  the  \ 
aboveinentioned  apparatus.  If  we  place  small  paper  riders  (or 
thin  fibres  of  wood)  upon  the  string  and  sing  the  tone  which 
belongs  to  it  over  the  mouth  of  the  tube,  the  paper  figures  w'ill 
begin  to  dance.  The  tone  of  a  tuning  fork  placed  upon  a  sound- 
ing board  will  also  cause  a  string  of  the  same  pitch  with  it 
to  resound,  and  the  paper  figures  will  dance.  The  same  effect 
will  be  produced  when  the  tuning  fork  is  held  at  a  distance  of 
several  feet  from  the  string.  The  pitch,  moreover,  of  the  glass 
tube  exerts  an  influence  similar  to  that  which  takes  place  when 
the  ear  is  armed  with  a  resonator.  If  we  make  the  string  of 
such  a  lensTth  that  its  fundamental  tone  agrees  with  the  tone  of 
the  tube,  then  the  tone  of  the  string  will  be  particularly  full  and 
powerful. 

§8. 

MATHEMATICAL  APPENDIX, 

Tiaving  particular  reference  to  the  rnechanisin  of  curved 
rnemhranes. 

In  the  following  we  presuppose  a  membrane  of  circular  form, 
having  inextensible  meridian  lines,  and  tense  elastic  fibres  ;  we 
assume  also  that^  the  pressure  of  the  air  acts  upon  one  of  the 
surfaces  of  this  membrane,  and  that,  on  the  other  hand,  there  is 
present  a  force  g  acting  upon  its  centre  in  the  direction  of  sym- 
metry. 

Then  in  order  to  understand,  as  shown  in  the  preceding 
section,  how  the  pressure  of  the  air  produces  the  strongest  resul- 
tants in  the  centre  of  a  feebly  curved  membrane  (provided  the 
membrane,  through  the  action  of  its  elastic  circular  fibres,  lias 
assumed  the  same  form  which  the  pressure  of  the  air  would  give 
to  it,  were  the  elastic  tension  of  the  circular  fibres  wanting),  let 
us  take  into  consideration  the  following  propositions. 

In  Fig.  10,  page  50,  let  ah  be  a  diameter,  c  the  middle  point 
of  the  firm  border  of  the  membrane,  and  y  the  centre  of  the 
membrane,  which  centre  the  force  fg  draws  in  the  direction  of 
the  axis.  The  meml)i-ane  may  have  assumed  the  form  indicated 
by  the  curved  line  merely  through  the  influence  of  the  tension 
of  its  elastic  circular  fibres  and  be  thus  in  permanent  equilibrium. 


MECHANISM    OF   THE    OSSICLES   OF   THE    EAR,  63 

We  will  next  presuppose  that  the  air  presses  equally  upon  both 
sides  of  the  membrane. 

Now  it  is  a  well  known  general  law  in  mechanics,  that  in 
every  case,  where  the  law  of  the  conservation  of  forces  comes 
into  play,  permanent  eqnilibrium  takes  place  only  when,  among 
all  the  positions  which  the  movable  system  can  assume,  the  con- 
dition of  equilibrium  is  that  one  in  which  the  measure  of  inter- 
nal and  external  forces  acting  upon  it  is  a  maximum. 

This  law  is  applicable  to  the  membrane  in  question  and  it 
follows  that  in  its  condition  of  equilibrium  the  total  amount  of 
force  exerted  by  the  contraction  of  the  elastic  circular  fibres  must 
be  a  maximum  in  comparison  with  that  which  may  be  exerted 
in  any  of  the  other  forms  into  which  the  membrane  could  pass 
while  the  position  of  the  point/"  remains  unchanged. 

Should  then  any  other  force  whatever  give  the  membrane  an- 
other form,  while  the  position  of  the  point  h  remains  unchanged, 
the  work  accomplished  by  this  force  must  necessarily  be  of  a 
positive  character,  since  the  quantity  of  the  power  of  the  tension 
exerted  by  the  membrane  must  be  increased  by  this  transition. 

The  same  would  hold  true  if  the  membrane  were  brought  into 
the  position  afh,  not  by  means  of  its  elasticity  but  through  the 
pressure  of  the  more  condensed  air  above  it,  exerting  a  ioreafg 
upon  its  centre/".  In  this  case  the  membrane  must  necessarily 
assume  such  a  form  that  the  force,  exerted  by  the  expansion  of 
the  more  condensed  air  above,  would  be  a  maximum.  This  latter 
would  however  take  place,  if  the  volume  of  the  air  contained 
above  the  membrane  and  the  prolonged  plane  a  h  became  a 
maximum.  It  follows  again,  that  if  another  force  were  em- 
ployed in  order  to  change  the  form  of  the  meuibrane  in  any 
way  whatever,  the  volume  of  the  more  condensed  air  above 
would  necessarily  become  less  and  the  additional  force  would 
have  to  produce  positive  results. 

Now,  if  the  form  afh^  produced  by  the  elastic  force,  be 
exactly  the  same  as  that  which  the  pressure  of  the  air  produces 
and  if  the  former  counterbalances  the  force  g  and  the  latter  the 
force  y,  then  will  the  membrano  without  change  of  form  be  in 
equilibrium,  through  the  simultaneous  action  of  the  elastic  circu- 
lar fibres  and  the  pressure  of  the  air,  aTid  will  counterbalance  the 


64  MECHANISM   OF   THE    OSSICLES   OF   THE   EAR. 

force  g  and  y  which  acts  at  tlie  point  f.  If  the  position  which 
the  membrane  assumes,  when  in  a  position  of  eqnilibriuiu 
through  the  action  of  elastic  forces  (the  centre  of  the  membrane 
being  at/"),  differs  from  tliat  wliich  the  pressure  of  the  air  pro- 
duces (the  position  of  the  centre  being  still  the  same),  then  the 
membrane  under  the  united  influence  of  both  forces  will  come 
to  a  state  of  rest  in  a  position  varying  from  either  of  the  other 
two  positions.  In  this  position,  neither  the  elastic  forces  nor 
the  pressure  of  the  air  will  have  exerted  the  maximum  of  their 
power,  that  is,  what  they  are  capable  of  doing  when  the  centre 
is  aty. 

Taking  chen,  as  a  starting-point,  that  form  which  the  mem- 
brane receives,  when  the  force  g  is  infinitely  great  and  when,  as 
a  result,  the  radial  fibres  must  be  extended  in  a  straight  line, 
and  then  supposing  the  force  g  to  be  gradually  diminished  until 
the  centre  of  the  membrane  has  advanced  to  the  point  y,  we 
shall  find  that  the  membrane  exerts  a  force  which  increases  in 
value  from  zero  to  a  value  of  G,  and  that  this  value  is  dependent 
upon  the  position  of  the  point /". 

Let  then  G^  represent  the  ft)rce  exerted  in  this  case,  when 
the  elasticity  alone  acts,  G^  when  the  pressure  of  the  air  alone 
acts,  and  G.2  when  both  forces  act  simultaneously ;  then 
^2  <  ^0  +  ^i5  except  in  the  case  where  the  elasticity  and  the 
pressure  of  the  air  give  the  same  form  to  the  membrane. 

Starting  from  the  position  where  these  quantities  are  equal 

to  zero,  then,  if  the  length  g  f  be  represented  by  A,  during  a 

first  period  must 

dO,  <  ^0  +  ^^' 
d  h         d  h         d  h  ' 

because  otherwise  from  the  outset  the  following  would  have 

been  true : 

Oq_G<,  +  G\. 

Now,  however,  the  above  differential  quotients  equal  the  re- 
sulting forces  which  tend  to  draw  the  centre  of  the  meinbrane 
toward  c. 

The  force  with  which  the  elasticity  of  the  membrane  (taken 
alone)  acts,  is  represented  by  g: 

"      dh 


mechanism:  of  the  ossicles  of  the  ear.  65 

Bj  y  is  represented  tlie  force  with  which  the  pressure  ot  the 
air,  taken  alone,  acts  : 

^       dh 
and  the  force,  with  which  the  pressure  of  the  air  and  the  elas- 
ticity together  act,  we  will  indicate  bj  ^  +  y„  : 

dh 
It  follows  from  the  above  equation  that  in  the  smaller  curves 
of  the  membrane 

9  +  7"  <  g  +  7, 
or 

ro  <  7, 
provided  the  form  of  the  inembrane,  in  which  the  condition  of 
equilibrium  exists,  is  not  the  same  for  the  simple  force  of  elas- 
ticity and  for  the  pressure  of  the  air ;   Q.  E.  D. 

To  determine  the  form  of  a  membrane  made  tense  hy  the 
pressure  of  the  air  alone^  and  containing  inextensihle  radial 
fibres. 

Let  3  be  a  given  portion  of  the  axis  of  the  membrane,  and  r 
the  radius  of  the  circle  in  which  a  plane,  passing  through  a  va- 
riable point  near  the  end  of  z  perpendicularly  to  the  axis,  cuts 
the  membrane.  The  volume  which  lies  between  two  such  planes, 
corresponding  to  the  values  z  and  3  +  d  z,  whose  dilFerence  is 
infinitely  small,  is  therefore 

■K  r^  dz 

The  entire  volume  -y,  between  the  membrane  and  the  plane 
which  passes  through  its  circle  of  attachment,  is  therefore 

^  _     I  irr^dz 


if  for  the  centre  of  the  membrane  z  =  o  and  for  tlie  circum- 
ference z  —  a. 

Let  jy  represent  the  excess  of  the  pressure  of  the  air,  upon  the 
upper  surface  of  the  membrane,  over  the  pressure  of  the  air  on 
the  under  surface,  and  G  the  effects  of  a  force  acting  upon  the 
centre  of  the  membrane  and  in  a  direction  parallel  to  its  axis, 
then  the  combined  effect  of  this  force  and  the  pressure  of  the  air 
is  equal  to 


66  MECHANISM   OF  THE   OSSICLES   OF  THE   EAR. 

The  conditions  which  permit  of  equilibrium  are  that  this 
quantity  should  be  a  maximum  while  the  length  of  the  radial 
fibres  remains  the  same ;  the  element  of  this  length  has  been 
given  in  the  equation 

ds^  =  dr''  +  dz\ 

Considering  then  r  as  an  independent  variable^  then  must 


or,  according  to  the  principles  of  differential  calculus,  if  we  dif- 
ferentiate z : 

dz  dSz 


dO    ,                  r  /     ddz  dr  dr 

dz  —  rrp      /    /    2  — _ 

dz  (1     dr  (dz 


j/l-^(^) 


?y = 0. 


Partially  integrated  we  have  the  following  result,  if  we  make 
6  s,  at  the  periphery  of  the  membrane,  equal  0,  and  in  its  cen- 
tre equal  (5  Sq  '- 


dz 

J  n  dr  , 

i^  +  ^p  A .  V  fe.. 

dz 


/-(tr 


dz 


-h  Trp 


^f''^'^'-''\^^y'- 


Since  then  dz^  and  dz  are  absolute  quantities  independent  of 
each  other,  it  follows  that  those  magnitudes  which  are  multi- 
plied by  them  equal  zero  ;  hence, 

1.  For  the  centre  of  the  membrane  : 


dQ  .  dr^ 

+    TTOX  =     0 


\/'  +  {^) 


MECHANISM    OF   THE    OSSICLES   OF   THE   EAR.  67 

2.  For  its  surface , 

dz 

|/l  +(§)' 

where  C  is  understood  to  represent  a  constant.  In  the  cen- 
tral point  of  the  membrane  r  =  o,  and  -^=  cot.  a,  a  repre- 
senting the  angle  so  designated  in  Fig,  10.  For  this  point 
therefore  equation  No.  2  becomes  reduced  to  C=  —  A  cos  a  and 
the  equation  No.  1  gives  for  the  same  point 

+  Tz  p  A  cos  a  =  0. 

d  z 

When  we,  on  the  other  hand,  represent  the  amount  r  at  the 

border  of  the  membrane  by  B,  and  let  -£r  =  tang  i3,  as  in  Fig. 

10,  then  according  to  equation  No.  2 

R^  —  X  cos  p  =  G  =  —  %  cos  a 

consequently 

R^  =  A  {cos  j3  —  cos  a) 

and  the  force  g 

_  dO  _        Tz  p  R^  cos  a 
'  dz  ~~       cos  (3  —  cos  a 

as  given  in  the  previous  section. 

Again,  from  equation  No.  2  follows : 

or 

r'  +  A  cos  a  , 

dr 


i 


A*  —  {r"  +  A  cos  af 


This  is  an  elliptical  integral  which  we  restore  to  the  normal 
form  when  we  make 


dr  =  — 


2  "k  sin  —- .  cos  u 


2  X  sin  -—  .  sin  u  d  u 


68  MECHANISM   OF  THE   OSSICLES   OF  THE   EAR. 

then  will 

1  —  2  siji^  —  wi'  u 
2 
du 


l/^A 


dz  =  —  1/  i/1    —  sin^ — sin^  u 


i 

Or,  if  we  follow  Legendre, 


do 


Fu 


Eu  — 


and  place 
then  is 


i/ 


4/1  —  jC  ^i<^  <•> 


V  1  —  x^sin^  udu 


X  —  sitv — 
2 


A    (  ) 

-2~^2  Eu  —  Fo)'r  +  Const. 


=  2  A  /  -^  .xcos  u 


\' 


At  the  same  time  we  easily  lind  the  length  of  the  arc  of  the 
radial  iibres — 


1/"^^" 


By  means  of  Legendre's  tables,  which  give  the  values  of  E(^ 
and  i^w  for  all  values  of  |-  and  w,  which  correspond  to  whole 
degrees,  we  can  construct  the  form  of  this  curve  in  the  easiest 
possible  manner.  For  arbitrary  values  of  a  and  w  the  values 
oi  E  (ji  and  F  w  can  be  computed  according  to  well-known 
methods. 

Fig.  12  shows  a  perfect  curve  of  this  kind,  drawn  from  one  axis- 
point  to  the  other,  in  which  the  value  180°  —  40°  =  140°  is 
given  to  the  angle  a,  corresponding  to  the  form  of  the  membrana 
tympani.  The  axis-point  may  represent  the  centre  of  the  mem- 
brane. Each  point  of  the  arms  of  the  curve  extending  from  a 
could  correspond  to  the  circumference  of  the  membrane,  as  far 


MECHANISM    OF   THE   OSSICLES   OF   THE   EAR, 


69 


Fig.  12. 

as  that  point  wliere  the  curve,  descending  in  the  direction  of  h, 
meets  and  crosses  itself  again.  The  membrana  tympani  itself 
corresponds  only  to  a  small  part  of  this  curve. 

For  the  present,  I  shall  defer  the  special  description  and  dis- 
cussion of  my  experiments  (referred  to  in  foot-note  of  page  8) 
on  "  resonance-tones  "  in  the  living  ear,  because  I  hope  to  obtain 
better  means  of  producing  deep  and  simple  tones  than  I  have 
had  thus  far,  and  in  order  that  the  experiments  may  be  better 
performed. 


